Luther Schwarz currently has a balance of $838.55 in his savings account. __________ years ago, Luther deposited $500 in his savings account, which pays an annual interest rate of 9 percent, compounded annually.
A) 8
B) 7
C) 6
D) 5

Question

Quizplus · Accepted Answer

To find the number of years, we need to use the formula for compound interest:
A = P(1+r/n)^(nt), where A is the ending balance, P is the principal (initial deposit), r is the annual interest rate expressed as a decimal, n is the number of times interest is compounded per year, and t is the number of years.

We know P is $500, r is 0.09, n is 1 (compounded annually), and A is $838.55. We can solve for t:

$838.55 = $500(1+0.09/1)^(1t)
$838.55/$500 = 1.6771 = (1.09)^t
ln(1.6771) = t*ln(1.09)
t = ln(1.6771)/ln(1.09) ≈ 6

Therefore, Luther deposited the $500 about 6 years ago. The best choice is C) 6.

Luther Schwarz Currently Has a Balance of $838