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%
Responses
12%
12%
10%
10%
6%
6%
8%
Answers
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%.
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%.