Theresa invested $5,000 in an account she expects will earn 7% annually. Approximately how many years will it take for the account to double in value? (Round the number of years to the nearest whole number.)
A) 8
B) 9
C) 10
D) 11
E) 12

Question

Quizplus · Accepted Answer

To double the initial investment of $5,000, the account must be worth $10,000. We can use the formula for compound interest:

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

where:
A = final amount (in this case, $10,000)
P = principal (initial investment, $5,000)
r = annual interest rate (7% or 0.07)
n = number of times interest is compounded per year (we'll assume it's compounded annually, so n = 1)
t = number of years

Plugging in the values, we get:

10000 = 5000(1 + 0.07/1)^(1t)

Simplifying:

2 = (1.07)^t

Taking the log of both sides:

log(2) = t log(1.07)

Solving for t:

t = log(2) / log(1.07) ≈ 10.24

Rounding to the nearest whole number, it will take approximately 10 years for the account to double in value. So the best choice is C) 10.

Theresa Invested $5,000 in an Account She Expects Will Earn