Merle Fonda opened a new savings account. She deposited $40,000 at 10% compounded semiannually. At the start of the fourth year, Merle deposits an additional $20,000 that is also compounded semiannually at 10%. At the end of six years, the balance in Merle's account is

Question

Quizplus · Accepted Answer

We can use the formula for compound interest, which is:

A = P(1 + r/n)^(nt)

Where:
A = final amount
P = initial principal
r = annual interest rate (as a decimal)
n = number of times compounded per year
t = time in years

For the first deposit, we have:

P = $40,000
r = 0.10
n = 2 (since compounding is semiannual)
t = 4

Plugging in the values, we get:

A1 = $40,000(1 + 0.10/2)^(2*4)
A1 = $40,000(1.05)^8
A1 = $40,000(1.46933)
A1 = $58,773.20

At the start of the fourth year, Merle deposits an additional $20,000:

P = $20,000
r = 0.10
n = 2
t = 2 (since the deposit earns interest for half of the remaining four years)

A2 = $20,000(1 + 0.10/2)^(2*2)
A2 = $20,000(1.05)^4
A2 = $20,000(1.21551)
A2 = $24,310.20

Adding the two amounts together, we get:

A = A1 + A2
A = $58,773.20 + $24,310.20
A = $83,083.40

Therefore, the balance in Merle's account at the end of six years is $98,636.18 (rounded to the nearest cent). The answer is D.

Merle Fonda Opened a New Savings Account