Business Mathematics and Statistics: Interest, Time Value and Descriptive Measures
Business Mathematics and Statistics tests numerical fluency: simple and compound interest, present and future value, annuities, ratios, averages, dispersion, probability and interpretation of results. Most marks come from setting up the calculation correctly and stating the interpretation.
Interest and time value
Simple interest: I = P x r x t. Compound amount: A = P(1 + r/n)^(nt), where n is compounding periods per year. Effective annual rate = (1 + r/n)^n - 1. Present value: PV = FV / (1 + r)^n. Annuity present value: PV = PMT x [1 - (1 + r)^-n] / r. Use the periodic rate and the total number of periods consistently.
Descriptive statistics
Mean is sensitive to outliers; median is robust; mode is the most frequent value. Standard deviation measures spread around the mean. Coefficient of variation equals standard deviation divided by mean and allows comparison across different scales.
Worked example
PKR 100,000 is deposited at 8% compounded quarterly for two years. Periodic rate = 8% / 4 = 2%; periods = 4 x 2 = 8. A = 100,000 x (1.02)^8 = 100,000 x 1.171659 = PKR 117,165.90. Interest earned is PKR 17,165.90. The effective annual rate is (1.02)^4 - 1 = 8.243%, higher than the nominal 8% because of quarterly compounding. Using 8% for eight periods would badly overstate the answer.
Probability and interpretation
Add probabilities for mutually exclusive events and multiply for independent events. Expected value is the probability-weighted average of outcomes. Always state units and whether the figure is a rate, an amount or a percentage.
Traps
Mixing nominal and periodic rates, using simple interest when compounding is stated, forgetting to double the periods, and misreading the median for an even number of observations, where it is the average of the two middle values.