Suppose you invest $1,000 in a mutual fund. If the annual return of that fund is 5 percent, how many years will it take before your fund is worth $2,000?
A) 10 years
B) 14 years
C) 20 years
D) never

Question

Quizplus · Accepted Answer

We can use the formula for compound interest to solve this problem:
A = P(1 + r/n)^(nt)
Where:
A = the final amount (in this case $2,000)
P = the initial amount (in this case $1,000)
r = the annual interest rate (in this case 5% or 0.05)
n = the number of times interest is compounded per year (for simplicity, we can assume it's compounded annually, so n = 1)
t = the number of years
Substituting the given values, we get:
$2,000 = $1,000(1 + 0.05/1)^(1t)
Simplifying:
2 = (1.05)^t
Taking the natural logarithm of both sides:
ln(2) = t*ln(1.05)
t = ln(2)/ln(1.05)
t ≈ 13.86 years
Therefore, it will take approximately 14 years for your fund to be worth $2,000.

Suppose You Invest $1,000 in a Mutual Fund