Your bank balance is exactly $10,000. Three years ago you deposited $7,938 and have not touched the account since. What annually compounded rate of interest has the bank been paying?

Question

Quizplus · Accepted Answer

To solve this problem, we can 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, t is the number of years, and n is the number of times the interest is compounded per year. We know that A=$10,000, P=$7,938, t=3, and n=1 (since the problem states "annually compounded"). We can then solve for r as follows:

$10,000=$7,938(1+r/1)^(1*3)
$10,000/$7,938=(1+r)^3
1.258689=(1+r)^3
Taking the cube root of both sides, we get:
1.070849 = 1+r
r = 1.070849 - 1
r = 0.070849 = 7.0849%
Therefore, the bank has been paying an annual interest rate of approximately 8.00% (rounded to the nearest hundredth). The correct answer is C).

Your Bank Balance Is Exactly $10,000