Question

3. Julie and Bill Stevens are purchasing a tractor and will need a $50,000 loan. The contractual rate is currently 7% with five equal annual payments. Their lender uses the add-on method of calculating interest.

a. What are the annual payments?

b. What is the effective interest rate of the loan?

c. What is the effective interest rate if the lender uses the remaining balance method of calculating interest? Explain the difference from problem b.

Answer 1

Given Information:

Loan Amount = $50,000

Interest Rate = 7%

Tenure or Period of Loan – 5 Years

Repayment Cycle – 5 Annual payments

Method of Calculation of Interest – Add-on Method

Note: Add-on Method – Method of calculating the interest to be paid by the borrower upfront on the loan amount. That is interest is calculated on the initial loan amount for the entire period of loan.

(a) Annual Payments:

Annual Payments = (Loan Amount + Total Interest)/Repayment Cycle

Total Interest = (Loan amount * Interest rate * Period of loan)

                      = $50,000*7%*5

   = $17,500

Annual Payments = ($50,000+$17,500)/5

    = $13,500

(b) Effective Interest rate of Loan:

Effective Interest rate = ((Total Interest /Loan Amount)*100/Number of years)

                                  = (($17,500/$50,000)*100/5)

                            = 7%

(c) Effective Interest rate when the Remaining balance method is used:

Effective interest rate = ((Total Interest /Loan Amount)*100/Number of years)

Total Interest = Total Annual Repayments – Loan Amount

Annual Repayments under remaining balance method = Loan Amount / Present Value Annuity Factor

Present Value Annuity Factor (PVAF) of 5 years at 7% = 4.10 (Can be obtained from PVAF Table)

Annual Repayments under remaining balance method = $50,000/4.1

                                                                                       = $12,195

Total Annual Repayments = Annual repayments * Number of Repayments

                                        = $12,195*5

                                  = $60,975

Total Interest = $60,975 - $50,000

                      = $10,975

Effective Interest Rate = (( $10,975/$50,000)*100/5)

   = 4.39%

Therefore, under add-on method, the effective interest rate of 7% is higher as compared to the Effective interest rate of 4.39% under Remaining balance method. Add-on method Loans are substantially more expensive than the Remaining balance method Loans.