Question

Shirley, a recent college​ graduate, excitedly described to her older sister the ​$1,940 ​sofa, table, and chairs she found today.​ However, when asked she could not tell her sister which interest calculation method was to be used on her​ credit-based purchase. Calculate the monthly payments and total cost for a bank loan assuming a​ one-year repayment period and 14 percent interest. Now assume the store uses the​ add-on method of interest calculation. Calculate the monthly payment and total cost with a​ one-year repayment period and 12 percent interest. Explain why the bank payment and total cost are lower even though the stated interest rate is higher.

The monthly payment for a bank loan assuming​ one-year repayment period and 14 percent interest is ​$

Answer 1

Based on the Monthly Installment Loan Tables,

At 14% Shirley's monthly payment for the simple interest loan would be $174.1926( $89.79  X 1.940) for a total loan cost of ($174.1926 x 12) & $2090.3112.Monthly Cost= $2090.3112/12= $174.1926

Using the Interest ($ 232.8 as calculated below) to the principal amount($ 1,940) and dividing by the total number of payments( $2172.8/12) yields a payment amount of $ 181.0666.Shirley would pay a monthly payment of $181.0666

Interest = principal X  Interest rate X Time

Interest=$1940 X 0.12 X 1=232.8

With the same loan terms,Shirley will save monthly $ 6.8734 ($181.0666-$174.1926) or a total  of $ 82.4808,if she find a loan using the simple interest method.The add on method is more expensive because it assumes that you have the entire loan balance outstanding for the entire period; rather than a decreasing balance,as is taken into account by the simple interest loan.