Calculate the amount if 20,000 is compounded annually for 2 years and 4 months @12% p.a.

Question

Calculate the amount if 20,000 is compounded for 2 years and 4 months @12% p.a.

I try solving this problem but my answer was wrong.

We apply formula, $A = P(1 + R)^n $ $= 20,000(1 + .12)^{2 + 4/12}$ $= 20,000(1.12)^{2.3334}$

Calculating this on a calculator gives around 26055.8 but this is not correct answer. Answer is given to be 26091.52 which is around 35 units greater. I want to know what's the mistake in my work?

I know a different method to solve it, and can solve it on my own, just posting it to know mistake in this method.

Answer 1

The only way I can arrive at $26091.52$ is giving 12% interest the first two years and then 12%/3 = 4% for the next four months. I don't see how this makes any sense at all, but it is true that $20000 \cdot 1.12^2 \cdot 1.04 = 26091.52$.

The original answer, obtained by $20000 \cdot 1.12^{28/12}$, seems correct to me.

Answer 2

12% of 20000 is 2400 so 2400 interest will be earned the first year. Since this is 'compounded annually' that is added to the principal making 22400.

12% of 22400 is 2688 so the interest for the second year wouold be 2688. But this is only invested for 4 months or 1/3 of the second year so we divide by 3: 2688/3= 896. Adding that to the 22400 we will have 22400+ 896= 23296 at the end of one year and four months.