Question

What rate of interest, compounded semiannually, will allow a college savings fund with an initial deposit of $60,000 to yield $159,000 after 10 years?(1 point)

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the rate of interest, compounded semiannually, we can use the formula for compound interest:

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

Where:
A = the final amount ($159,000)
P = the principal (initial deposit) ($60,000)
r = the annual interest rate (unknown)
n = the number of times the interest is compounded per year (2 for semiannually)
t = the number of years (10)

Plugging in the known values, we have:

$159,000 = $60,000(1 + r/2)^(2*10)

Simplifying further:

2.65 = (1 + r/2)^20

To isolate (1 + r/2), we take the 20th root of both sides:

(1 + r/2) = ∛2.65 ≈ 1.082

Now, subtract 1 from both sides to solve for r/2:

r/2 ≈ 1.082 - 1 = 0.082

Finally, multiply both sides by 2 to find the annual interest rate:

r ≈ 2 * 0.082 = 0.164

The rate of interest, compounded semiannually, that will allow the college savings fund to yield $159,000 after 10 years is approximately 16.4% per year.