Question

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

Answer (a)

Loan Amount = $50,000/-

Rate of Interest= 7%

Time Period = 5 years

In the case of add on method total yearly interest is calculated at the beginning same is added to the installment payable, however interest is to be converted in Monthly basis if installment is payable on monthly

so in this case,

Annual interest @7% on $50000 for one year

Interest = 50000*0.07*1= $3500

Principal Payment = Total Loan Amount/ Number of Installment

= $50000/5

= $10,000

So, Required Annual Payment=( Principal + Interest)= ($10000+$3500)= $ 13,500 p.a.

Answer ( b) Let r be the effective rate of interest

Yearly Installment=$ 13,500

Loan Amount= $50,000/-

Number of Installment = 5

13500= 50000*r*((1+r)^5)/((1+r)^5-1)

r*((1+r)^5)/((1+r)^5-1)= 13500/50000

r*((1+r)^5)/((1+r)^5-1)=0.27

by putting r= 10% we get

r*((1+r)^5)/((1+r)^5-1)= 0.26380

and by putting r= 11% we get

r*((1+r)^5)/((1+r)^5-1)= 0.27057

by the method of interpolation

we get

r= 10+(0.27-02638)/(0.27057-0.26380)*1=10+0.92= 10.92% (Approx)

Answer (c).

In the case of reducing balance Method interest is calculated on outstanding balances of principal at the beginning of each period. Since Payment term is annual so effective rate would be same i.e.. 7%

It is Difference from part ( b) because Interest calculated on the part( a ) is always on initial loan amount however in part (c) principal amount of loan is reducing after the payment of each installment.so effecting rate of interest is more in part (b) as compare to part (c)