If a borrower promises to pay you $1,900 9 years from now in return for a loan of $1,000 today,what effective annual interest rate is being offered?
A) 5.26%
B) 7.39%
C) 9.00%
D) 10.00%

Question

Quizplus · Accepted Answer

To calculate the effective annual interest rate, we can use the formula:

(1 + i)^n = PV/FV

where i is the effective annual interest rate, n is the number of years, PV is the present value (loan amount), and FV is the future value (the amount to be paid back).

Plugging in the values, we get:

(1 + i)^9 = 1900/1000
(1 + i)^9 = 1.9

Taking the 9th root of both sides, we get:

1 + i = 1.076
i = 0.076 or 7.6%

Therefore, the effective annual interest rate being offered is 7.39%, which is closest to option B.

If a Borrower Promises to Pay You $1,900 9 Years