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Question

Suzette and Bridgett are sisters. Suzette deposits $30,000 at the start of each year for 15 years into an account that earns 8.5% compounded annually. Bridgett also makes annual deposits of $30,000 into a similar account that pays 8.5%.  Which sister will accumulate the highest account balance after 15 years? Assume no withdrawals are made.

Answer 1

To solve this problem, we can use the formula for the future value of an annuity:

FV = PMT x ((1 + r)^n - 1) / r

where FV is the future value of the annuity, PMT is the annual payment, r is the annual interest rate, and n is the number of years.

For Suzette, we have:

PMT = $30,000 r = 8.5% n = 15

FV = $30,000 x ((1 + 0.085)^15 - 1) / 0.085 = $744,847.84

For Bridgett, we have the same values:

PMT = $30,000 r = 8.5% n = 15

FV = $30,000 x ((1 + 0.085)^15 - 1) / 0.085 = $744,847.84

Both sisters will accumulate the same account balance after 15 years. This is because they are making the same annual payments into accounts that earn the same interest rate and are compounded annually. Therefore, both sisters will have a future value of $744,847.84 at the end of 15 years.

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