Interest Rates and Investments An electronics store advertises the following fin

Question

Interest Rates and Investments

An electronics store advertises the following financing arrangement: "We don't offer confusing interest rates. We just divide your total cost by 10 and can pay that amount each month for a year." The first payment is made at the date of the sale and the remaining payments are made at the monthly anniversary thereafter. Calculate the annual interest rate the store's customers are paying on the loan. Assuming that the store allows (as many do) no repayment for the first year, what is the annual interest rate on the loan?

Explanation / Answer

a)

Let the total cost be 120

Monthly payment = total cost/10

Monthly payment = 120/10

Monthly payment =12

nper = 12

Monthly interest rate = rate(nper,pmt,pv,fv,1)

Monthly interest rate = rate(12,12,-120,0,1)

Monthly interest rate = 3.50%

Effective Annual interest Rate = (1+Monthly interest rate )^n - 1

Effective Annual interest Rate = (1+3.5%)^12 - 1

Effective Annual interest Rate = 51.11%

b)

Let the total cost be 120

Monthly payment = total cost/10

Monthly payment = 120/10

Monthly payment =12

nper = 12

Monthly interest rate = rate(nper,pmt,pv,fv,1)

Monthly interest rate = rate(12,12,-120,0,1)

Monthly interest rate = 3.50%

Effective Annual interest Rate = (1+Monthly interest rate )^n/2 - 1

Effective Annual interest Rate = (1+3.5%)^12/2 - 1

Effective Annual interest Rate = 24.45%

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