Installment Buying Stereo Shack sells a stereo system for ...

Installment Buying Stereo Shack sells a stereo system for $\$ 600$ down and monthly payments of $\$ 30$ for the next 3 years. If the interest rate is 1.25$\%$ per month on the unpaid balance, find
a. the cost of the stereo system.
b. the total amount of interest paid.

Key Concepts

Down Payment and Financed Amount

A down payment is the upfront part of the purchase price paid at the time of purchase, which reduces the total amount that must be financed. The financed amount is the remaining balance that the buyer agrees to pay over time, and it is on this amount that interest is typically charged, a key component in determining the total cost of the purchase.

Interest Rate per Period

The interest rate per period is the rate at which interest accrues on the unpaid balance of a loan during each payment interval, such as monthly. In installment buying, this periodic rate is crucial because it is applied to the outstanding balance, causing the interest cost to change over the life of the loan as the principal is gradually reduced.

Annuity and Present Value

Annuities involve a series of equal payments made at regular intervals and are used in finance to determine the present value of ongoing payments. When evaluating installment purchases, the concept of annuities helps in determining the equivalent lump sum value of future payments, taking into account the time value of money and the interest rate applied.

Finance Charge and Total Cost

The finance charge represents the total cost of borrowing, including all interest accrued over the term of the financing arrangement. It is the additional expense incurred beyond the principal amount financed. Calculating the finance charge and adding it to the down payment and principal repaid helps in understanding the true total cost of an installment purchase.

Installment Buying

Installment buying is a financing method where a customer makes an initial down payment and then pays the remainder of the purchase price in a series of scheduled payments over time. This method often involves additional finance charges or interest, reflecting the cost of credit, and is common in consumer purchases like electronics and vehicles.

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