Comparing two-year deposit schemes for a tailoring unit
A tailoring unit in Coimbatore has Rs 80,000 of surplus funds that it will not need for two years, when it plans to buy a computerised sewing machine. Bank A offers a two-year cumulative deposit at 8.4% per annum compounded quarterly. Bank B offers 8.2% per annum compounded monthly. A cooperative bank offers 8.6% per annum compounded half-yearly but requires the money to remain for three years. The unit's accountant says Bank B is best because its monthly compounding 'adds interest more often', while the owner prefers Bank A because 8.4% is a higher headline rate. The machine can be postponed by one year if the three-year cooperative deposit is chosen; money withdrawn after two years from Bank A could be reinvested for the third year at 7% per annum compounded annually. Assume no tax and no withdrawal penalties.
1. Compute the effective annual rate for Bank A and Bank B. Which bank actually offers the higher effective return, and does the accountant's reasoning hold?
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For Bank A, the quarterly rate is 0.084/4 = 0.021. Effective annual rate = (1.021)^4 - 1 = 1.08668 - 1 = 0.08668, or 8.67%.
For Bank B, the monthly rate is 0.082/12 = 0.0068333. Effective annual rate = (1.0068333)^12 - 1 = 1.08515 - 1 = 0.08515, or 8.52%.
Bank A offers the higher effective return. The accountant's reasoning is incomplete: more frequent compounding helps, but it does not automatically overcome a lower nominal rate. The nominal rate and the compounding frequency must be combined through the effective annual rate.
2. Calculate the maturity value under Bank A and Bank B after two years. Give a recommendation consistent with the two-year constraint.
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Bank A: 80,000(1.021)^8. Since (1.021)^8 is about 1.18088, the maturity value is about 80,000(1.18088) = Rs 94,470.
Bank B: 80,000(1.0068333)^24. Since (1.0068333)^24 is about 1.17756, the maturity value is about 80,000(1.17756) = Rs 94,205.
Bank A produces about Rs 265 more after two years. Given the two-year cash need, Bank A is the better choice unless there is a non-numerical reason to prefer Bank B. The difference is small, so liquidity and bank reliability should also be checked.
3. Evaluate the cooperative option against the route of depositing in Bank A and reinvesting the maturity value for one year at 7% compounded annually. Which is better in rupee terms, and what non-numerical factors should the unit weigh?
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Cooperative bank for three years: 80,000(1.043)^6. Since (1.043)^6 is about 1.28737, the maturity value is about 80,000(1.28737) = Rs 102,990.
Bank A then reinvestment: Rs 94,470(1.07) = Rs 101,083.
The cooperative option is better by about Rs 1,907. However, it requires a third year of lock-in and assumes the machine can indeed be postponed. The comparison also assumes the 7% reinvestment rate is actually available and certain. The unit should weigh liquidity, credit risk of the cooperative bank, possible price changes for the sewing machine, and the cost of being unable to respond to an emergency. The numerical advantage is modest relative to these risks.