Ashley deposited $20,000 in an investment account on the day her son was born to help pay for tuition when he goes to college

Answer:

7. rate of return is 9.93%

8, number of years is 7.6375 years

Explanation:

7. Compute rate of return

FW = $20,000 * (F/P, i, 17)

using (F/P, i, n) = (1 + i)ⁿ

$100,000 = $20,000 * (1 + i)¹⁷

(1 + i)¹⁷ = 5

raising 1 /17 power on both sides

1 + i = 5^(1/17) = 1.0993

i = 1.099299 - 1 = 0.0993 = 9.93%

rate of return is 9.93%

8. Compute number of years

Annual deposit = X

Future Worth = 10X

FW = X * (F/A, i, n)

10X = X * (F/A, i, n)

(F/A, i, n) = 10      ----- eq 1

Compute (F/A, i, n) using [(1 + i)ⁿ - 1] / i

(F/A, 8%,n) = [(1 + 0.08)ⁿ - 1] / 0.08 = [(1.08)ⁿ - 1] / 0.08     ---- eq 2

Equating eq 1 and eq 2

[(1.08)ⁿ - 1] / 0.08 = 10

[(1.08)ⁿ - 1] = 0.8

(1.08)ⁿ = 1.8

taking logs of both sides, base 10

n * log(1.08) = log(1.8)

n = log(1.8) / log(1.08) = 0.255273 / 0.033424 = 7.6375

number of years is 7.6375 years