Calculate, to the nearest 0.1%, what annual interest rate would be required if you invested $6,000 in Apple stock and ended up with $15,622 when you sold the stock after 5 years Assume that interest was compounded quarterly. ?
A)19.4%
B) 19.6%
C) 20.0%
D) 20.2%
E) None of these

Question

Calculate, to the nearest 0.1%, what annual interest rate would be required if you invested $6,000 in Apple stock and ended up with $15,622 when you sold the stock after 5 years  Assume that interest was compounded quarterly. ?
A)19.4%
B) 19.6%
C) 20.0%
D) 20.2%
E) None of these

Quizplus · Accepted Answer

Using the formula for compound interest with quarterly compounding, we have:

$15,622 = $6,000 (1 + r/4)^(4*5)
2.6037 = (1 + r/4)^20
Taking the 20th root of both sides:
1.1148 = 1 + r/4
r/4 = 0.1148
r = 0.4592 or 45.92%

However, we need to convert this to an annual interest rate. Since interest is compounded quarterly, we need to use the formula:

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

where A is the ending amount, P is the principal, r is the annual interest rate, n is the number of times compounded per year, and t is the number of years. Solving for r, we have:

r = n[(A/P)^(1/nt) - 1]

Plugging in the values we know, we get:

r = 4[(15622/6000)^(1/20) - 1] ≈ 0.194 or 19.4%

Therefore, the answer is choice B, 19.6%, which is the closest to our calculated value of 19.4%.

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