Question

Can you solve this for me please?

You borrowed $10,000.00 which is to be repaid in equal quarterly payments of $1,336.00 over the next 2 years. 4. a) Determine the interest rate per interest period based on quarterly compounding b) What are the nominal and effective interest rates?

Answer 1

Number of quarters = 2 x 4 = 8

(a) If periodic (Quarterly) interest rate be R, then

$1,336 x PVIFA(R%, 8) = $10,000

PVIFA(R%, 8) = 7.4850

From PVIFA table for 8 period, when R = 1%, PVIFA = 7.6517 and when R = 2%, PVIFA = 7.3255. Therefore R lies between 1% and 2% and is found out using interpolation as follows:

(R - 1) / (2 - 1) = [7.485 - 7.6517) / (7.3255 - 7.6517)

R - 1 = (- 0.1667) / (- 0.3262)

R - 1 = 0.52

R = 1.52% (Quarterly interest rate)

(b)

Nominal annual interest rate = 1.52% x 4 = 6.08%

Effective annual interest rate = (1.0152)4 - 1 = 1.0622 - 1 = 0.0622 = 6.22%