Question

You worked very hard during the summer, and now you are paid $5,000 as your compensation. Now you would like to invest all of them into a fund so that you can spend them after 5 years. You have 2 funds to choose from:

1. Fund A promises 8% annual interest payment without reinvestment

2. Fund B promises 7% annual interest payment with reinvestment of interest

Which one would you choose? Please state clearly your criteria and the formulas you use to reach that decision.

Answer 1

Given:
Principal = $5000
time = 5 years

Fund A promises 8% annual interest without reinvestment, that means it uses simple interest. And fund B promises 7% annual interest with reinvestment of interest, that means it uses compound interest.

1. So let us find the amount after 5 years if you invest in fund A. We have simple interest formula, that is:

Where,
A = Amount at the end of 5 years
P = Principal amount invested
R = Rate of interest
T = Time in years

Substituting the values, we get:

Therefore, if you invest in Fund A you will get $7,000 at the end of 5 years.

2. If you invest in Fund B. We have compound interest formula:

Where,
A = Amount at the end of 5 years
P = Principal invested
r = rate of interest
t = time in years

Substituting the values, we get:

Therefore, your account will have $7,012.76 if you invest in fund B.

If you compare the final amount in both funds you can see that Fund B is better, since it gives $12.76 more that Fund A. So you should chose fund B because it gives more return than fund A even though the interest rate is lower.