Which of the following schemes of computing interest yields the maximum interest for a year?
- AInterest compounded every year at 24% p.a.
- BInterest compounded monthly at 2% per month.
- CInterest compounded per quarter 6% per quarter.
- DInterest compounded every six months at 12% for every 6 months
Solution & Step-by-step Explanation
The frequent compounding of interest always yields a higher effective annual interest rate for the same nominal annual interest rate because interest earns interest more frequently.
Let's look at the compounding frequency for each scheme over 1 year (12 months):
Option A: Compounded annually ⟹ 1 time a year.
Option D: Compounded semi-annually ⟹ 2 times a year.
Option C: Compounded quarterly ⟹ 4 times a year.
Option B: Compounded monthly ⟹ 12 times a year.
Since monthly compounding has the highest compounding frequency per year, it reinvests the accumulated interest the most times, resulting in the highest effective annual yield.
Let's look at the compounding frequency for each scheme over 1 year (12 months):
Option A: Compounded annually ⟹ 1 time a year.
Option D: Compounded semi-annually ⟹ 2 times a year.
Option C: Compounded quarterly ⟹ 4 times a year.
Option B: Compounded monthly ⟹ 12 times a year.
Since monthly compounding has the highest compounding frequency per year, it reinvests the accumulated interest the most times, resulting in the highest effective annual yield.