Question

Julia is exactly 28 years and 3 months old right now. He found his soulmate and just decided he wants to get married when he will be exactly 29 years and 8 months old. He hasn't started to save up money yet (present value of his portfolio is zero). If he saves $2,300 per month for 12 months, starting in one month from now, assuming a 0.65% interest rate per month, how much will he have approximately at the date he finally marries?

A) $26,508.63
B) $28,608.74
C) Nothing, because if he didn't save any so far, he won't save until the wedding date
D) $32,464.26
E) $36,114.84
F) None of the above

Answer 1

The correct answer is B) $28,608.74, which is the future value of Julia's savings after saving $2,300 per month for 12 months at a 0.65% monthly interest rate, using the future value of an annuity formula.

Step-by-step explanation:

The question asks us to calculate the future value of a savings account with monthly deposits and compound interest. To solve this, we can use the future value of an annuity formula:

FV = P × { [(1 + r)^{n} - 1] / r }, where FV is the future value, P is the monthly payment, r is the monthly interest rate, and n is the total number of deposits.

Julia plans to save $2,300 monthly for 12 months, and the monthly interest rate is 0.65%. Converted to decimal form, the interest rate (r) is 0.0065. The number of deposits (n) is 12 since she wants to save for 12 months. The formula becomes:

FV = $2,300 × { [(1 + 0.0065)^{12} - 1] / 0.0065 }

FV

is approximately

$28,608.74

, which means the correct answer is B) $28,608.74.