The EZ Credit Company offers to loan a college student $6,400 for school expense

Question

The EZ Credit Company offers to loan a college student $6,400 for school expenses. Repayment of the loan will be in monthly installments of $272.04 for 30 months. The total repayment of money is $8,161, 20, which includes the original $6,400, $1, 235.34 in interest charges, and $525.86 for a required life insurance policy covering the amount of the loan. Assume monthly compounding of interest. What nominal interest rate is being charged on this loan The nominal interest rate that is being charged on this loan is % per year.

Explanation / Answer

Amount of loan = $6400

No. of month for payment (n) = 30

Monthly Installment (P) = $272.04

Monthly interest rate (R) = ?

Now,

Amount of loan = present value of all monthly installments

6400 = P*(1-1/(1+R)^n)/R

6400 = 272.04*(1-1/(1+R)^30)/R

At R = 1%

Present value of all monthly installments = $7020.729

At R = 2%

Present value of all monthly installments = $6092.732

Thus, as per the method of interpolation,

R = 1% + ((PV of EMI at 1% - Loan amount)/( PV of EMI at 1% - PV of EMI at 2%))*(2%-1%)

R = 1% + ((7020.729 - 6400)/( 7020.729 – 6092.732))*(2%-1%)

R = 1.65%

Thus,

Annual nominal interest rate = 12*R

Annual nominal interest rate = 19.8%

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