Question

4 years ago, you invest by putting 1500 in an account. 3 years ago, you put in another 800. Past two years, you put in 500$ each year. Today you have balance of 4124.17$. What interest rate did you earn, compounded annually? Show your work

Answer 1

Suppose that the compound interest rate remained same throughout that period.

Let the compound rate =x

According to the question,

4124.17= 1500(1+x)⁴ + 800(1+x)³ + 500(1+x)² + 500(1+x)

Now we need to make some assumptions to solve this equation.The assumption is that x is a small value and we expand it using taylor series to only the first term of x

4124.17= 1500(1+4x) + 800(1+3x) + 500(1+2x) + 500(1+x)

=> 4124.17= 1500+800+1000 + 9900x

9900x= 824.17

=> x=0.0832

= 8.32%