Two Years to ₹70,000: Choosing Between Savings, FD and RD
Harleen studies in Class 10 at a government school in Nabha. Her elder sister Simran has saved ₹60,000 from a summer job and wants to buy a ₹70,000 laptop-and-course package exactly 24 months from today. Their bank offers three products: a savings account at 2.7% a year, a fixed deposit at 6.8% a year compounded yearly (early closure allowed only with a 1% penalty on the interest rate), and a recurring deposit at 6.5% a year into which Simran could pay an amount every month. A man who visits their street promises to 'double the money in three years' if Simran hands over ₹60,000 in cash and accepts a handwritten receipt from his unregistered firm. Simran's employer may transfer her to another city in about 14 months. The family's emergency fund is only ₹5,000, and Simran does not want to lock away every rupee she has.
1. Does putting the full ₹60,000 in a 24-month fixed deposit get Simran to ₹70,000? Show the arithmetic and state the gap.
Read the worked answer
Yearly compounding means the balance is multiplied by 1.068 twice:
- 60,000 × 1.068 = ₹64,080 after year 1
- 64,080 × 1.068 = ₹68,437.44 after year 2
- Gap to the goal = 70,000 − 68,437 = ₹1,563 short
A simple-interest check gives the same verdict: 60,000 × 6.8% × 2 = ₹8,160, so ₹68,160 - still short, and slightly lower than the compounded figure, which is why the bank's 'per year' rate must be applied for two years, not just added once.
So the FD alone fails by about ₹1,563. Two further points matter for the judgement. First, the shortfall is small, so a small monthly top-up or shifting ₹1,600 more into the deposit at the start closes it. Second, if Simran closes the FD at 14 months because of the transfer, the rate drops to 5.8% (6.8% minus the 1% penalty rate) for the run period, so the 24-month figure is only valid if she actually stays to maturity. A transfer does not require her to close the FD, but the family's tiny emergency fund makes early closure tempting, so some money must stay liquid.
2. Design a mix that reaches ₹70,000 in 24 months while keeping at least ₹15,000 reachable for emergencies. Show approximate maturity values and the trade-offs.
Read the worked answer
Plan: ₹40,000 in a 24-month FD + ₹1,000 a month into an RD, keeping ₹20,000 in savings.
- FD: 40,000 × 1.140624 = ≈ ₹45,625
- RD: total deposits = 1,000 × 24 = ₹24,000. A standard approximation of RD interest is P × [n(n+1)/2] × r/12 = 1,000 × 300 × 0.065/12 ≈ ₹1,625, giving a maturity of ≈ ₹25,625
- Combined: 45,625 + 25,625 = ≈ ₹71,250, a buffer of about ₹1,250 over the goal
Why this works: ₹20,000 stays in the savings account, so the family's ₹5,000 emergency fund is not the only cushion and Simran can meet the ₹1,000 instalments for 20 of the 24 months from that balance if her income stops. The remaining four instalments come from her salary. The RD instalments are small enough to continue from another city, and the FD can simply be allowed to mature.
Trade-offs to state: the RD depends on a monthly commitment; a missed instalment usually attracts a small penalty and the RD may be closed early at a lower rate; a transfer means branch formalities. Keeping money in a savings account at 2.7% costs returns, but it buys liquidity, which is exactly what this family lacks. Locking all ₹60,000 in the FD would have failed the goal anyway and left the household with ₹5,000 in an emergency.
3. Simran is tempted by the 'double the money in three years' offer. Using the Rule of 72 or compound arithmetic, explain the return the offer implies and the checks she should apply before saying yes.
Read the worked answer
The maths: doubling in 3 years needs a rate r where (1 + r)³ = 2, so r ≈ 26% a year. The Rule of 72 gives 72 ÷ 3 = 24% a year - the same ballpark. Compare that with the bank's 6.8% FD: the offer promises roughly four times a bank FD, in a scheme run by an unregistered firm with a handwritten receipt.
Why that is a red flag: no genuine low-risk product pays 24–26% guaranteed. A 'guaranteed' high return plus cash collection plus no proper documentation is the classic pattern of a Ponzi scheme, where early investors are paid from later investors' money until the flow stops.
Checks before saying yes:
- Is the firm registered with RBI, SEBI or the state authority for the activity it claims? Ask for the registration number and verify it independently; RBI publishes lists of authorised entities.
- Is the money protected? Deposit insurance (DICGC) covers bank deposits up to ₹5 lakh per depositor per bank - it does not cover private firms, chit schemes run without permission, or cash receipts.
- Insist on a proper agreement, a printed receipt with the firm's details, and payment through banking channels, never cash.
- Treat guarantees, pressure to decide today, and 'bring your neighbours' pitches as warning signs.
- Guidance: the ₹60,000 is her sister's entire savings for a specific goal, so capital protection outranks a speculative extra return. Refuse the offer and report the agent to the bank branch or the local police if he persists.