Question

1) To borrow $1,500, you are offered an add on interest loan at 8.4 percent with 12 monthly payments. Compute the 12 equal payments.

2) Use the amount you borrowed and the monthly payments you computed to calculate the APR of the loan. Then, use that APR to compute the EAR of the loan.

1-?

2-?

Answer 1

1. Add on interest loan is one in which the interest is calculated by simply multiplying the interest rate with the principal and then multiplying with the number of years to repayment. This amount is then divided by the total number of payment periods. This interest is then added to the principal amount.

Principal P = 1500

Add-on interest rate = 8.4%

number of payments N = 12

Total interest = 1500 * 8.4% = $126

Total Amount = principal + interest

                      = 1500 + 126

                       = $1626

Monthly or 12 equal payments = 1626 / 12 = $135.50

2. APR of the loan can be calculated from excel or calculator as below:

N = 12

PV = 1500

PMT = - 135.50

FV = 0

CPT I = 1.2632%

APR = I *12 = 1.2632 * 12 = 15.159%

Effective annual rate = ( 1+ APR / 12)¹² - 1

                                  = ( 1+ 0.15159 / 12 )¹² - 1

                                  = ( 1 + 0.012632)¹² - 1

                                   = 1.1625781 - 1

                                  = 0.1625781

                                  = 16.26%

APR = 15.16%
EAR = 16.26%