Question

Jaquan hopes to earn $1500 in interest in 2.9 years time from $120,000 that he has available to invest. To decide if it's feasible to do this by

investing in an account that compounds semi-annually, he needs to determine the annual interest rate such an account would have to offer for him
to meet his goal. What would the annual rate of interest have to be? Round to two decimal places.

Answer 1

To determine the annual rate of interest that Jaquan needs to earn $1500 in interest in 2.9 years, we can use the formula for future value of an investment:

FV = PV x (1 + r)^n

where:

FV = Future Value (the amount Jaquan wants to earn in 2.9 years, which is $1500)

PV = Present Value (the amount Jaquan has available to invest, which is $120,000)

r = Annual interest rate (the rate the account must offer to earn $1500 in 2.9 years)

n = Number of periods (the number of years the money is invested, which is 2.9 years)

We can solve for r by rearranging the formula:

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

Substituting the values given:

r = ($1500 / $120,000) ^ (1/2.9)

r ≈ 4.92%

So, the annual interest rate the account must offer to earn $1500 in 2.9 years is approximately 4.92%.

Explanation: