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

Question

Quizplus · Accepted Answer

To double the initial investment, the account needs to earn another $5,000 (100% increase). Since the account is expected to earn 7% annually, we can use the following formula to find the number of years it will take to double:
$5,000 x 1.07^n = $10,000
Simplifying the equation:
1.07^n = 2
Taking the logarithm of both sides:
n log(1.07) = log(2)
n = log(2) / log(1.07)
n ≈ 10
Therefore, it will take approximately 10 years for the account to double in value. The closest whole number to 10 is C (10).

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