- 2069 Poush
Simple vs compound interest; number of deposits
Short answer
Simple interest is charged on principal only; compound interest on principal plus accumulated interest. To accumulate Rs 20,00,000 with Rs 50,000 monthly deposits at 10% nominal annual rate compounded monthly, about 35 deposits are needed (last may be slightly smaller).
Differentiate between simple interest and compound interest. How many deposits of Rs. 50,000 each should be made per month so that the future amount will be Rs. 20,00,000 if the bank interest rate is 10% per year?
Simple vs compound interest
| Basis | Simple interest | Compound interest |
|---|---|---|
| Interest charged on | Original principal only | Principal plus interest already earned |
| Formula | I = P·i·n, F = P(1 + i·n) | F = P(1 + i)^n |
| Growth | Linear (straight line) | Exponential |
| Interest per period | Same every period | Increases every period |
| Use | Short-term loans, bills | Banks, long-term investment, engineering economy |
| Value after n > 1 | Smaller | Larger |
Example: Rs 1,000 at 10% for 3 years gives F = 1,300 (simple) and F = 1,331 (compound).
Number of deposits
Assumption: 10% per year is nominal, compounded monthly; deposits are made at the end of each month.
- Monthly i = 10% / 12 = 0.8333%
- F = A (F/A, i, n), so (F/A, 0.8333%, n) = F / A = 20,00,000 / 50,000 = 40
- [(1 + i)^n − 1] / i = 40
- (1 + i)^n = 1 + 40 × 0.008333 = 1.33333
- n = ln(1.33333) / ln(1.008333) = 0.28768 / 0.00830 = 34.67
Check: n = 34 gives F = 50,000 × 39.119 = Rs 1,955,940 (short); n = 35 gives F = 50,000 × 40.445 = Rs 2,022,239.
Answer: about 35 monthly deposits of Rs 50,000 (34.67 ≈ 35; the last deposit can be slightly smaller).
✓ Answer checked by Claude Opus 5.5 (high effort)
Related questions
- Monthly deposits with quarterly compounding, future amount · Engineering Economics, chapter 2
- Nominal vs effective rate; simple vs compound deposit · Engineering Economics, chapter 2
- Loan 120,000: number of installments and rate · Engineering Economics, chapter 2
- Car loan interest rate and lump sum at year 3 · Engineering Economics, chapter 2
- Deposit now to draw growing monthly amount · Engineering Economics, chapter 2
- Capital recovery cost; interest on motorbike loan · Engineering Economics, chapter 2
- EPS and book value; ABC project Rs 6,00,000 · Project Engineering, chapter 6
- EPS and book value; Rs 10,00,000, 3500 shares · Project Engineering, chapter 6
- EPS and book value; capital Rs 5,00,000 · Project Engineering, chapter 6
- EPS; total capital Rs 15,00,000 · Project Engineering, chapter 6