Question

Michael wants to invest an inheritance of ​$28,000 for one year. His credit union offers 5.57​% for a​ one-year term or 5.52​% for a​ six-month term.

​(a) How much will Michael have after one year if he invests at the​ one-year rate?
​(b) How much will Michael have after one year if he invested for six months at a time at 5.52​% each​ time?
​(c) What would the​ one-year rate have to be to yield the same amount of interest as the investment described in part​ (b)?

Answer 1

Michael will have $29,559.60 after one year at the one-year interest rate. If he invests at the six-month interest rate twice, he will have $29,549.55 after one year. The equivalent one-year rate to match the six-month interest compounded is approximately 5.534%.

Step-by-step explanation:

Michael wants to invest an inheritance of $28,000. To calculate how much he will have after one year at the one-year rate:
$28,000 × (1 + 0.0557) = $29,559.60.

- For the six-month term repeated twice:
First six months: $28,000 × (1 + 0.0552/2) = $28,772.80
Second six months: $28,772.80 × (1 + 0.0552/2) = $29,549.55

- Equivalent One-Year Rate

To find the one-year rate that gives the same amount of interest as the six-month term chosen twice, we need to solve the equation $28,000 × (1 + r) = $29,549.55, which gives r = 5.534%.