Question

Serena has a $39,800 debt that she wishes to repay 6 years from today; she has $31,454 that she intends to invest for the 6 years. What rate of interest will she need to earn annually in order to accumulate enough to pay the debt? (Round answer to 0 decimal places, eg. 7\%.) Rate of interest %

Answer 1

Serena needs to earn an annual interest rate of approximately 4% on her investment of $31,454 to accumulate $39,800 in 6 years.

Step-by-step explanation:

Serena needs to determine the rate of interest she will need to earn annually on her investment of $31,454 to grow it to $39,800 in 6 years. To find the rate, we can use the future value formula for compound interest:

FV = PV * (1 + r) ^n

Where FV is the future value of the investment ($39,800), PV is the present value of the investment ($31,454), r is the annual interest rate (expressed as a decimal), and n is the number of years the money is invested (6 years).

We rearrange the formula to solve for r:

r = (FV/PV) ^(1/n) - 1

Plugging in the numbers:

r = ($39,800 / $31,454) ^(1/6) - 1

r ≈ 0.04 or 4%

Hence, Serena needs to earn an annual interest rate of approximately 4% to reach her goal.