Question

Lee Holmes deposited $15,000 in a new savings account at 9% interest compounded semiannually. At the beginning of year 4, Lee deposits an additional $40,000 at 9% interest compounded semiannually. What is the balance in Lee's account?

Answer 1

Answer:

The balance in Lee's account is $72,680.5

Explanation:

The formula to calculate amount for a compound interest is given as,

A = P(1+r)^n

Since the interest is compounded semiannually, at the end of year 3, the amount in Lee's account would be = 15000(1+0.09)^6 = 15000(1.09)^6 = $25,156.50

At the beginning of year 4, she deposits an additional $40,000

At the end of year 4, the amount in Lee's account would be = 40,000(1+0.09)^2 = 40,000(1.09)^2 = $47,524

Lee's balance = $25,156.50 + $47,524 = $72,680.5

Answer 2

Answer:

$77,528.75

Explanation:

we can divide this calculation into two time periods, the first one will last 3 years:

future value = present value (1 + r)ⁿ

• n = 6
• present value = $15,000
• r = 9% / 2 = 4.5%

future value = $15,000 (1 + 4.5%)⁶ = $19,533.9 ≈ $19,534

the second period will also last 3 years:

future value = present value (1 + r)ⁿ

• n = 6
• present value = $19,534 + $40,000 = $59,534
• r = 9% / 2 = 4.5%

future value = $59,534 (1 + 4.5%)⁶ = $77,528.75