Question

The nominal rate on Sarah’s loan is 7.250%. If the interest is compounded monthly, what rate of interest is Sarah actually paying? a. 7.250% b. 7.496% c. 7.510% d. 8.700%

Answer 1

The correct Option is B. 7.496%

Explanation:

Nominal interest rate (r) = 7.250%

The effective annual rate Sarah is actually paying (R) :

`R = (1 + (r)/(12))^(12)-1 = (1 +(0.0725)/(12))^(12) -1\\\\\implies R= 1.0749583 -1\approx 0.07496`

So, actual rate which Sarah is paying = 0.07496 × 100

= 7.496%

Hence, The correct Option is B. 7.496%

Answer 2

The effective annual rate (r') is ...

r' = (1 + r/12)¹² -1 = (1 +.0725/12)¹² -1 ≈ 1.0749583 -1

r' ≈ 7.496% . . . . . matches selection b.