Which of the following schemes of computing interest yields the maximum interest for a year?
Interest compounded monthly at 2% per month.
Comparing Interest Schemes for Maximum Yield
To determine which scheme yields the maximum interest over a year, we calculate the Effective Annual Rate (EAR) for each option. The EAR represents the actual annual rate of return taking compounding into account.
Calculating Effective Annual Rate (EAR)
The formula for EAR is:
$ \text{EAR} = \left(1 + \frac{r}{n}\right)^n - 1 $
Where:
- r is the nominal annual interest rate.
- n is the number of times interest is compounded per year.
Alternatively, if the rate per compounding period (i) is given, and the number of periods per year is n:
$ \text{EAR} = (1 + i)^n - 1 $
Option 1: Annual Compounding
Rate = 24% per year (compounded annually).
$ \text{EAR} = (1 + 0.24)^1 - 1 = 0.24 $
EAR = 24.00%
Option 2: Monthly Compounding
Rate = 2% per month.
Number of compounding periods per year (n) = 12.
Rate per period (i) = 0.02.
$ \text{EAR} = (1 + 0.02)^{12} - 1 \approx 1.26825 - 1 $
EAR ≈ 26.83%
Option 3: Quarterly Compounding
Rate = 6% per quarter.
Number of compounding periods per year (n) = 4.
Rate per period (i) = 0.06.
$ \text{EAR} = (1 + 0.06)^4 - 1 \approx 1.26248 - 1 $
EAR ≈ 26.25%
Option 4: Semi-annual Compounding
Rate = 12% per 6 months.
Number of compounding periods per year (n) = 2.
Rate per period (i) = 0.12.
$ \text{EAR} = (1 + 0.12)^2 - 1 = 1.2544 - 1 $
EAR = 25.44%
Comparison of EARs
Comparing the calculated EARs:
| Scheme | Compounding Frequency | Rate per Period | Effective Annual Rate (EAR) |
| 1 | Annually | 24% | 24.00% |
| 2 | Monthly | 2% | ≈ 26.83% |
| 3 | Quarterly | 6% | ≈ 26.25% |
| 4 | Semi-annually | 12% | 25.44% |
Conclusion
The scheme with the highest Effective Annual Rate (EAR) yields the maximum interest. Based on the calculations, Option 2 (Interest compounded monthly at 2% per month) provides the highest EAR of approximately 26.83%.
Similar Questions
On a certain sum, rate of interest per annum for the first two years is 4%. The rate of interest for next four years is 6% and for the next three years is 8%. If total simple interest earned at the end of 9 years is ₹ 1120, then the sum is:
A certain sum becomes ₹ 650 at the end of one year and ₹ 676 at the end of second year. The compound interest sum is:
Important Questions from Interest
Amar borrowed Rs. 10000 from Sachin at simple interest. After 4 years, Sachin received Rs. 5000 more than the amount given to Amar on loan. Find the rate of interest.
Simple interest accrued on the amount of Rs.14,000 is Rs. 1260 at the rate of 3 % per annum for t years. What would be the compound interest accrued on the same amount for the same years at 10 % per annum compounded annually?
Rishu deposited an amount of Rs. 950 at Compound Interest. The amount gets doubled of itself after 4 years. What will be the amount after 12 years?
On a certain sum, rate of interest per annum for the first two years is 4%. The rate of interest for next four years is 6% and for the next three years is 8%. If total simple interest earned at the end of 9 years is ₹ 1120, then the sum is:
A certain sum becomes ₹ 650 at the end of one year and ₹ 676 at the end of second year. The compound interest sum is:
