Question

You plan to put money into a bank account that earns a 7.2% APR with monthly compounding. You plan to invest $630 at the end of each half‐year, as well as a to‐be‐determined initial amount today. Under this plan, how much must you invest today to have a total account balance of $38,000 in 8 years?

Answer 1

$13,867

Step-by-step explanation:

the monthly interest = 7.2% / 12 = 0.6%

the effective semiannual rate = (1 + 0.6%)⁶ - 1 = 3.6544%

this is an ordinary annuity and its future value will be:

FV = semiannual payment x FV annuity factor

• semiannual payment = $630
• FV annuity factor, 3.6544%, 16 periods = 21.2303

FV = $630 x 21.2303 = $13,375

This means that you are $38,000 - $13,375 = $24,625

the present value = $24,625 / (1 + 3.6544%)¹⁶ = $13,867