Amanda invests a sum of money in a retirement account with a fixed annual interest rate of 7% compounded continuously. After 19 years, the balance reaches $31,446.94. What was the amount of the initial investment?

The amount of initial investment is $8695.34

Explanation:

The amount initially invested by calculated using the Present Value formula given below:

PV=FV / (1+r) ^n

FV=future value of investment=$31,446.94

r=rate of return=7%

n=number of years = 19 years

PV=$31446.94 / (1+0.07) ^19

PV=$8695.34

The reason amount invested has increased significantly was that the principal is reinvested alongside interest, which means interest was earned from two streams, interest from the initial principal and interest on the interest. In essence, the power of compound interest is illustrated here