Question

Quarter-end payments of $1,480 are made to settle a loan of $32,260 in 8 years. What is the effective interest rate?

Answer 1

Information provided:

Quarterly payment= $1,480

Present value= $32,260

Time= 8 years*4= 32 quarters

The question is first solved by computing the nominal interest rate.

The nominal interest rate is computed by entering the below in a financial calculator:

PMT= 1,480

N= 32

PV= 32,260

Press the CPT key and I/Y to calculate the nominal interest rate.

The value obtained is 2.5169

Therefore, the nominal interest rate is 2.5169%*4= 10.07%.

Effective annual rate is calculated using the below formula:

EAR= (1+i/n)^n-1

Where i is the interest rate and n is the number of compounding periods in one year.

EAR= (1+0.1007/4)^4-1

        = 1.1046-1

        = 0.1046*100= 10.46%

Therefore, the effective annual rate is 10.46%.

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