I85PREP
⌘ K
MB Applied Math 40S study materials
MB Applied Math 40S study resources

MB Applied Math 40S practice questions

One question at a time. Build your MB Applied Math 40S understanding.

First 50 of 200 questions. Each one lists the choices, the correct answer, and an explanation. The checker at the top of this page saves progress in this browser when it is available.

Continue in the practice tool above to load more questions, 50 at a time.

Question 1Financial Mathematics

A payday loan of $400 is repaid 14 days later with a total charge of $56. What is the annual simple interest rate, using a 365-day year and treating the charge as interest?

  1. 26%
  2. 182.5%
  3. 365% Correct answer.
  4. 3.65%

Explanation

The interest rate for the 14-day period is 56/400 = 0.14, or 14%. Annualizing with simple interest multiplies by 365/14, giving 0.14 × 26.07 ≈ 3.65, which is about 365% per year. This shows how short-term fees convert to enormous annual rates.

Question 2Financial Mathematics

Which statement correctly describes how a credit card's grace period works?

  1. The grace period applies only to cash advances and balance transfers
  2. No interest accrues on new purchases if the previous balance was paid in full by the due date Correct answer.
  3. Interest is charged on every purchase from the day of purchase regardless of payment history
  4. The grace period is the time allowed after the due date before a late fee applies

Explanation

A grace period is an interest-free window on purchases that exists only when the previous statement balance was paid in full on time. Once a balance is carried, interest typically accrues from the transaction date. Cash advances normally have no grace period at all.

Question 3Financial Mathematics

An investment of $2,000 earns 5% per year compounded annually. What is the value after 3 years, to the nearest dollar?

  1. $2,315 Correct answer.
  2. $2,100
  3. $2,300
  4. $2,521

Explanation

Compound interest uses A = P(1 + i)^n with P = 2000, i = 0.05, and n = 3. Computing gives 2000 × 1.157625 = 2315.25, which rounds to $2,315.

Question 4Financial Mathematics

A car worth $18,000 depreciates at 12% per year. What is its value after 4 years, to the nearest dollar?

  1. $12,000
  2. $9,360
  3. $11,520
  4. $10,795 Correct answer.

Explanation

Declining-balance depreciation multiplies the value by (1 − 0.12) each year, so V = 18000(0.88)^4. Since 0.88^4 ≈ 0.5997, the value is about $10,795.

Question 5Financial Mathematics

A loan is repaid with equal payments at the end of every month. Which formula gives the present value of the loan if the monthly rate is i and there are n payments of R?

  1. PV = R × [1 − (1 + i)^(−n)] / i Correct answer.
  2. PV = R × n × (1 + i)
  3. PV = R / (1 + i)^n
  4. PV = R × [(1 + i)^n − 1] / i

Explanation

The present value of an ordinary annuity discounts each payment back to today and sums the geometric series. The result is R times the annuity factor [1 − (1 + i)^(−n)]/i. The future value formula instead accumulates payments forward.

Question 6Financial Mathematics

A student borrows $1,200 at 9% per year simple interest for 8 months. How much interest is owed?

  1. $72 Correct answer.
  2. $108
  3. $86
  4. $9

Explanation

Simple interest is I = Prt, with t measured in years. Here t = 8/12, so I = 1200 × 0.09 × (8/12) = $72. Using t = 8 would wrongly treat months as years.

Question 7Financial Mathematics

Which situation best illustrates the time value of money?

  1. Receiving $500 today is worth more than receiving $500 one year from now Correct answer.
  2. Prices of identical goods are the same in every store
  3. Saving money always reduces total wealth
  4. A $500 debt is equally costly whether paid today or next year at 0% interest

Explanation

Money available now can be invested or used to avoid borrowing, so it grows over time. Therefore a dollar today is worth more than a dollar in the future whenever the interest rate is positive. This principle underlies all discounting and compounding.

Question 8Financial Mathematics

A credit card charges 1.5% interest per month on the unpaid balance. What nominal annual rate compounded monthly does this represent?

  1. 19.56%
  2. 16.5%
  3. 1.5%
  4. 18% Correct answer.

Explanation

The nominal annual rate is the periodic rate multiplied by the number of periods per year. With 1.5% per month over 12 months, the nominal rate is 18%. The effective annual rate would be slightly higher because of compounding.

Question 9Financial Mathematics

An annuity pays $300 at the end of each quarter for 5 years, with interest at 8% per year compounded quarterly. Which expression gives the future value?

  1. 300 × [(1.02)^20 − 1] / 0.02 Correct answer.
  2. 300 × [(1.08)^5 − 1] / 0.08
  3. 300 × 20 × 1.02
  4. 300 × [1 − (1.02)^(−20)] / 0.02

Explanation

The quarterly rate is 0.08/4 = 0.02 and the number of payments is 4 × 5 = 20. The future value of an ordinary annuity is R × [(1 + i)^n − 1]/i, giving 300 × [1.02^20 − 1]/0.02.

Question 10Financial Mathematics

A $5,000 loan at 6% per year compounded monthly is repaid over 3 years. What is the monthly payment, to the nearest dollar?

  1. $152 Correct answer.
  2. $180
  3. $167
  4. $139

Explanation

Use PV = R × [1 − (1 + i)^(−n)]/i with i = 0.005 and n = 36. The annuity factor is about 32.871, so R = 5000/32.871 ≈ $152.

Question 11Financial Mathematics

An investment earns 6% per year compounded monthly. What is the effective annual rate, to two decimal places?

  1. 6.00%
  2. 6.50%
  3. 6.17% Correct answer.
  4. 5.84%

Explanation

The effective rate is (1 + r/m)^m − 1 with r = 0.06 and m = 12. Computing (1.005)^12 − 1 gives about 0.06168, or 6.17%. The effective rate exceeds the nominal rate because of monthly compounding.

Question 12Financial Mathematics

A credit card balance of $2,400 is charged 1.25% monthly interest. The cardholder pays $150 at the end of the month. What is the new balance?

  1. $2,310
  2. $2,430
  3. $2,250
  4. $2,280 Correct answer.

Explanation

Interest is 2400 × 0.0125 = $30, so the balance grows to $2,430 before the payment. Subtracting the $150 payment leaves $2,280.

Question 13Financial Mathematics

A machine costs $20,000 and depreciates at 15% per year on the declining balance. After how many full years does its value first fall below $10,000?

  1. 3 years
  2. 4 years
  3. 5 years Correct answer.
  4. 6 years

Explanation

The value after n years is 20000(0.85)^n, and we need 0.85^n < 0.5. Since 0.85^4 ≈ 0.522 and 0.85^5 ≈ 0.4437, the value first drops below half after 5 years.

Question 14Financial Mathematics

You deposit $200 at the end of each month into an account earning 4.8% per year compounded monthly. What is the balance after 4 years, to the nearest dollar?

  1. $11,200
  2. $10,556 Correct answer.
  3. $9,600
  4. $8,800

Explanation

The monthly rate is 0.048/12 = 0.004 and there are 48 deposits. Using FV = 200 × [(1.004)^48 − 1]/0.004 gives about $10,556, which exceeds the $9,600 of contributions because of interest.

Question 15Financial Mathematics

A loan of $10,000 at 9% per year compounded annually is repaid in 4 equal annual payments made at the end of each year. What is each payment, to the nearest dollar?

  1. $3,250
  2. $2,500
  3. $2,955
  4. $3,087 Correct answer.

Explanation

Set 10000 = R × [1 − 1.09^(−4)]/0.09. The annuity factor is about 3.2397, so R = 10000/3.2397 ≈ $3,087. Equal payments must exceed the simple principal share because of interest.

Question 16Financial Mathematics

A $1,000 investment grows to $1,210 in 2 years with annual compounding. What annual interest rate was earned?

  1. 21%
  2. 5%
  3. 11%
  4. 10% Correct answer.

Explanation

From 1000(1 + i)^2 = 1210 we get (1 + i)^2 = 1.21, so 1 + i = 1.1 and i = 10%. The rate is found by taking a square root, not by halving the total growth.

Question 17Financial Mathematics

A 25-year mortgage of $250,000 at 5.4% per year compounded semi-annually requires monthly payments. What periodic rate should be used in the payment formula?

  1. 5.4% per month
  2. 0.45% per month
  3. About 0.444% per month Correct answer.
  4. 0.225% per month

Explanation

Canadian mortgages compound semi-annually, so first find the equivalent monthly rate: (1 + 0.054/2)^(1/6) − 1. This gives about 0.00444, or roughly 0.444% per month, which is slightly less than simply dividing 5.4% by 12.

Question 18Financial Mathematics

Two banks offer the same nominal rate of 6%. Bank A compounds monthly and Bank B compounds annually. Which statement is true?

  1. Both have the same effective annual rate
  2. Bank A's effective rate equals its nominal rate
  3. Bank A's effective annual rate is higher than Bank B's Correct answer.
  4. Bank B's effective annual rate is higher than Bank A's

Explanation

More frequent compounding means interest is earned on interest sooner, so the effective rate rises with the compounding frequency. Bank A's effective rate is about 6.17%, while Bank B's is exactly 6%. The nominal rates are equal but the effective rates differ.

Question 19Financial Mathematics

A credit card advertises 19.99% per year compounded daily. What daily periodic rate is used, assuming a 365-day year?

  1. About 0.0555% per day
  2. About 1.666% per day
  3. About 0.1999% per day
  4. About 0.0548% per day Correct answer.

Explanation

The daily periodic rate is the nominal annual rate divided by 365, so 0.1999/365 ≈ 0.000548, or about 0.0548% per day. This rate is then applied to the balance each day.

Question 20Financial Mathematics

An investor deposits $1,500 now and $1,500 two years from now into an account earning 5% per year compounded annually. What is the balance immediately after the second deposit?

  1. $3,075
  2. $3,000
  3. $3,154 Correct answer.
  4. $3,225

Explanation

The first deposit grows for two years to 1500(1.05)^2 = $1,653.75, and the second deposit is added at its face value of $1,500. The total is $3,153.75, or about $3,154.

Question 21Financial Mathematics

A lease of $30,000 is amortized with monthly payments at 6% per year compounded monthly for 5 years. Approximately how much of the 60th payment reduces the principal?

  1. About $580
  2. About $150
  3. About $430
  4. About $396 Correct answer.

Explanation

The payment is about $580 per month. The balance just before the final payment is the present value of one payment, about $577, so interest that month is 577 × 0.005 ≈ $2.89. The principal portion is therefore about $580 − $2.89 ≈ $577, and the last payment nearly retires the loan.

Question 22Financial Mathematics

A savings plan deposits $100 at the beginning of each month for 10 years at 6% per year compounded monthly. Which expression gives the accumulated value?

  1. 100 × 120 × 1.005
  2. 100 × [1 − (1.005)^(−120)]/0.005
  3. 100 × [(1.005)^120 − 1]/0.005
  4. 100 × [(1.005)^120 − 1]/0.005 × 1.005 Correct answer.

Explanation

Deposits at the beginning of each period form an annuity due, whose future value is the ordinary annuity value multiplied by (1 + i). With i = 0.005 and n = 120, the expression is 100 × [(1.005)^120 − 1]/0.005 × 1.005.

Question 23Financial Mathematics

A borrower takes a $200,000 mortgage at 4.8% per year compounded monthly for 25 years. After 5 years of monthly payments, approximately what balance remains?

  1. About $160,000
  2. About $185,000
  3. About $171,600 Correct answer.
  4. About $150,000

Explanation

The monthly payment is about $1,144. The remaining balance is the present value of the 240 payments still to come, 1144 × [1 − (1.004)^(−240)]/0.004, which is roughly $171,600. Early payments are mostly interest, so the principal falls slowly.

Question 24Financial Mathematics

An item costs $1,200 cash or can be bought with 12 equal monthly payments of $110. What approximate monthly interest rate makes these options equivalent?

  1. About 10% per month
  2. About 1.4% per month Correct answer.
  3. About 2.5% per month
  4. About 0.83% per month

Explanation

Set 1200 = 110 × [1 − (1 + i)^(−12)]/i and solve numerically. The annuity factor must be about 10.909, which corresponds to i near 0.014, or roughly 1.4% per month. This is well above the 0.83% obtained by ignoring the time value of the payments.

Question 25Financial Mathematics

A retiree wants to withdraw $2,000 at the end of each month for 20 years from a fund earning 5.4% per year compounded monthly. Approximately how much must be in the fund at retirement?

  1. About $480,000
  2. About $293,000 Correct answer.
  3. About $360,000
  4. About $240,000

Explanation

The required amount is the present value of 240 monthly payments at i = 0.0045. The annuity factor is about 146.5, so PV ≈ 2000 × 146.5 ≈ $293,000, well below the $480,000 total of the withdrawals because the fund keeps earning interest.

Question 26Financial Mathematics

A payday lender advertises a fee of $15 for every $100 borrowed over a 14-day term. What simple interest rate does this fee represent for the 14-day period, expressed as a decimal?

  1. 1.5
  2. 0.015
  3. 0.15 Correct answer.
  4. 0.0015

Explanation

Simple interest rate equals interest divided by principal. Here the fee is $15 on a principal of $100, so the rate for the term is 15 ÷ 100 = 0.15, or 15% for the 14 days.

Question 27Financial Mathematics

Which statement correctly describes how compound interest differs from simple interest?

  1. Compound interest earns interest on previously earned interest, while simple interest earns interest only on the principal. Correct answer.
  2. Both earn interest only on the original principal but compound interest uses a lower rate.
  3. Simple interest earns interest on previously earned interest, while compound interest earns interest only on the principal.
  4. Compound interest applies only to loans, while simple interest applies only to savings.

Explanation

The defining feature of compounding is that each period's interest is added to the balance and then itself earns interest in later periods. Simple interest is always computed on the original principal alone, so growth is linear rather than exponential.

Question 28Financial Mathematics

An account pays 3% per year compounded quarterly. What periodic interest rate is applied each quarter?

  1. 0.012
  2. 0.03
  3. 0.0075 Correct answer.
  4. 0.12

Explanation

When a nominal annual rate is compounded quarterly, the annual rate is divided by four periods per year. Thus 3% ÷ 4 = 0.75%, written as the decimal 0.0075 per quarter.

Question 29Financial Mathematics

A student invests $800 at 4% per year simple interest. What is the total value of the investment after 3 years?

  1. $896 Correct answer.
  2. $864
  3. $832
  4. $899.89

Explanation

Simple interest is I = Prt = 800 × 0.04 × 3 = $96, and the accumulated value is principal plus interest, $800 + $96 = $896. Simple interest grows linearly, so the same $32 is added each year.

Question 30Financial Mathematics

Which expression gives the future value of a single deposit of $2,000 left for 5 years at 6% per year compounded annually?

  1. 2000(1.06)^5 Correct answer.
  2. 2000(1 + 0.06/5)^5
  3. 2000(1.6)^5
  4. 2000(0.06)(5)

Explanation

The compound-interest formula is FV = PV(1 + i)^n, where i is the rate per period and n is the number of periods. With annual compounding, i = 0.06 and n = 5, giving 2000(1.06)^5.

Question 31Financial Mathematics

A car worth $24,000 depreciates at 12% per year on the declining balance. What is its value after one year?

  1. $21,000
  2. $21,120 Correct answer.
  3. $23,880
  4. $2,880

Explanation

Declining-balance depreciation multiplies the current value by (1 − rate) each year. Here 24,000 × (1 − 0.12) = 24,000 × 0.88 = $21,120.

Question 32Financial Mathematics

Which statement best describes an ordinary annuity?

  1. A series of equal payments made at the end of each compounding period Correct answer.
  2. A series of payments that increase by a fixed dollar amount each period
  3. A single lump-sum payment made at the end of a term
  4. A series of equal payments made at the beginning of each compounding period

Explanation

An ordinary annuity consists of equal payments at regular intervals with each payment occurring at the end of its period. Payments at the beginning of each period define an annuity due, which is a different type.

Question 33Financial Mathematics

A loan of $1,500 is repaid with 6 equal monthly payments at 1% interest per month on the unpaid balance. Which statement about the payment schedule is true?

  1. The final payment is always larger than the earlier payments.
  2. Each payment covers the month's interest first, with the remainder reducing the principal. Correct answer.
  3. Each payment reduces the principal by an equal dollar amount before interest is charged.
  4. The interest portion of each payment increases as the loan is paid down.

Explanation

In an amortized loan the interest owed for the period is calculated on the outstanding balance and paid first; whatever remains of the level payment reduces the principal. Because the balance falls, the interest portion shrinks over time and the principal portion grows.

Question 34Financial Mathematics

An investment earns 3.6% per year compounded monthly. What monthly periodic rate should be used in the annuity formula?

  1. 0.0432
  2. 0.036
  3. 0.003 Correct answer.
  4. 0.3

Explanation

For monthly compounding the nominal annual rate is divided by 12. Thus 3.6% ÷ 12 = 0.3% per month, which as a decimal is 0.003.

Question 35Financial Mathematics

A sum of $5,000 is invested at 5% per year compounded annually. To the nearest dollar, what will it be worth after 10 years?

  1. $5,256
  2. $7,500
  3. $8,555
  4. $8,144 Correct answer.

Explanation

Use FV = PV(1 + i)^n = 5000(1.05)^10. Since (1.05)^10 ≈ 1.6289, the value is about $8,144.

Question 36Financial Mathematics

An account earns 8% per year compounded quarterly. To the nearest dollar, how much must be deposited now to have $10,000 in 6 years?

  1. $6,223 Correct answer.
  2. $6,301
  3. $6,210
  4. $9,600

Explanation

The present value is PV = FV(1 + i)^(-n), with i = 0.08/4 = 0.02 and n = 6 × 4 = 24 periods. So PV = 10000(1.02)^(-24) ≈ $6,223.

Question 37Financial Mathematics

A student deposits $150 at the end of each month into an account earning 6% per year compounded monthly. To the nearest dollar, what is the balance after 4 years?

  1. $8,150
  2. $9,842
  3. $8,109 Correct answer.
  4. $7,200

Explanation

Use the ordinary annuity future value FV = PMT[((1 + i)^n − 1)/i], with i = 0.005 and n = 48. The factor is about 54.06, so the balance is roughly $8,109.

Question 38Financial Mathematics

A couple wants to have $20,000 in 5 years. They will deposit an equal amount at the end of each month into an account earning 4.8% per year compounded monthly. To the nearest dollar, what monthly deposit is required?

  1. $287
  2. $333
  3. $295 Correct answer.
  4. $302

Explanation

Rearrange the annuity future value formula to PMT = FV × i / ((1 + i)^n − 1), with i = 0.004 and n = 60. The denominator is about 0.2705, giving a deposit of about $295 per month.

Question 39Financial Mathematics

A loan is repaid with level monthly payments. Which statement about the balance over the life of the loan is true?

  1. The outstanding balance falls quickly at first and more slowly later as interest grows.
  2. The outstanding balance falls by the same dollar amount every month.
  3. The outstanding balance stays constant until the final payment.
  4. The outstanding balance falls slowly at first and more quickly later as the interest share shrinks. Correct answer.

Explanation

With level payments, early payments are mostly interest because the balance is large, so little principal is retired. As the balance falls, interest charges shrink and a growing share of each payment reduces principal, so the balance drops faster over time.

Question 40Financial Mathematics

A credit card states an annual rate of 18% compounded monthly. What is the effective annual rate, to two decimal places?

  1. 19.56% Correct answer.
  2. 19.72%
  3. 1.50%
  4. 18.00%

Explanation

The effective rate is (1 + r/m)^m − 1 = (1 + 0.18/12)^12 − 1 = (1.015)^12 − 1 ≈ 0.1956, or 19.56%. It exceeds the nominal rate because each month's interest itself earns interest.

Question 41Financial Mathematics

A machine purchased for $40,000 depreciates at 20% per year on the declining balance. To the nearest dollar, what is its value after 3 years?

  1. $20,000
  2. $16,000
  3. $20,480 Correct answer.
  4. $25,600

Explanation

Each year the value is multiplied by 0.80, so after three years V = 40000(0.80)^3 = 40000 × 0.512 = $20,480. Declining-balance depreciation is exponential, not linear.

Question 42Financial Mathematics

A student borrows $3,000 at 12% per year compounded monthly and makes no payments for 18 months. To the nearest dollar, how much interest has accrued?

  1. $3,582
  2. $582 Correct answer.
  3. $540
  4. $621

Explanation

The balance is 3000(1.01)^18 ≈ $3,582, so the interest is that balance minus the $3,000 principal, about $582. Compounding raises the total above the simple-interest amount.

Question 43Financial Mathematics

A loan of $12,000 at 6% per year compounded monthly is to be repaid in 24 equal monthly payments. To the nearest dollar, what is the monthly payment?

  1. $548
  2. $620
  3. $532 Correct answer.
  4. $500

Explanation

Use PMT = PV × i / (1 − (1 + i)^(-n)), with i = 0.005 and n = 24. The discount factor gives a payment of about $532 per month.

Question 44Financial Mathematics

Two investment accounts are offered. Account X pays 5% per year compounded annually, and Account Y pays 4.9% per year compounded monthly. Which account has the higher effective annual rate?

  1. Account Y, at about 4.90%
  2. Account X, at exactly 5.00%
  3. Account Y, at about 5.01% Correct answer.
  4. The two accounts are exactly equal

Explanation

Account X's effective rate is 5%. Account Y's is (1 + 0.049/12)^12 − 1 ≈ 0.0501, or about 5.01%, so the more frequent compounding slightly outweighs the lower nominal rate.

Question 45Financial Mathematics

A retiree deposits $50,000 into a fund earning 4% per year compounded annually and withdraws $9,000 at the end of each year. To the nearest dollar, what is the balance immediately after the third withdrawal?

  1. $31,000
  2. $28,123 Correct answer.
  3. $29,247
  4. $23,000

Explanation

Track the balance year by year: after year 1, 50,000(1.04) − 9,000 = $43,000; after year 2, 43,000(1.04) − 9,000 = $35,720; after year 3, 35,720(1.04) − 9,000 = $28,123.

Question 46Financial Mathematics

A loan of $8,000 at 9% per year compounded monthly is amortized over 3 years. To the nearest dollar, how much of the first payment goes toward interest?

  1. $1,800
  2. $254
  3. $60 Correct answer.
  4. $720

Explanation

Interest for the first month is charged on the full outstanding balance at the periodic rate: 8,000 × (0.09/12) = 8,000 × 0.0075 = $60. The rest of the first level payment reduces principal.

Question 47Financial Mathematics

An investment doubles in value in 9 years with annual compounding. To the nearest hundredth of a percent, what annual interest rate was earned?

  1. 9.00%
  2. 7.20%
  3. 8.01% Correct answer.
  4. 11.11%

Explanation

Solve 2 = (1 + i)^9, so 1 + i = 2^(1/9) ≈ 1.0801. The annual rate is therefore about 8.01%.

Question 48Financial Mathematics

A loan of $15,000 at 7.2% per year compounded monthly is repaid with level monthly payments over 5 years. To the nearest dollar, what is the total interest paid over the life of the loan?

  1. $3,150
  2. $3,600
  3. $2,700
  4. $2,884 Correct answer.

Explanation

The monthly payment is about $298.41, so 60 payments total about $17,904. Subtracting the $15,000 principal leaves roughly $2,884 of interest.

Question 49Financial Mathematics

A student can pay $4,000 now for a course or pay $1,100 at the end of each of the next 4 years. Money can earn 6% per year compounded annually. Which choice is better in present-value terms, and by how much?

  1. Pay now, saving about $400
  2. Pay now, saving about $189 Correct answer.
  3. Pay in installments, saving about $189
  4. The two choices are equal in present value

Explanation

The present value of the four installments is 1100 × [1 − (1.06)^(-4)]/0.06 ≈ $3,811. Since this is less than $4,000, paying now is worse; the installment plan saves about $189 in present-value terms.

Question 50Financial Mathematics

A credit card charges 21% per year compounded monthly. A balance of $3,000 is carried with no payments for 4 months. To the nearest dollar, what is the balance at the end of that time?

  1. $3,210
  2. $3,175
  3. $3,213 Correct answer.
  4. $3,630

Explanation

The monthly rate is 0.21/12 = 0.0175, and the balance grows as 3000(1.0175)^4 ≈ $3,213. The compounding adds slightly more than four months of simple interest would.