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)

Responses

12%
12%

10%
10%

6%
6%

8%

Answer 1

[AI-generated answer — Bot GPT 3.5]

Let's assume the interest rate compounded semiannually is x.

After 10 years, the formula for compound interest is given by:
$60,000(1 + x/2)^{2*10} = $159,000

Solving this equation gives:
(1 + x/2)^20 = 159,000/60,000
(1 + x/2)^20 = 2.65

Taking the 20th root of both sides:
(1 + x/2) = 2.65^(1/20)
(1 + x/2) = 1.0834

Subtracting 1 from both sides:
x/2 = 0.0834

Multiplying both sides by 2:
x = 0.1668

Converting to a percentage:
x = 16.68%

Thus, the rate of interest, compounded semiannually, that will allow the college savings fund to yield $159,000 after 10 years is 16.68%.