498 Part 6 Working Capital Management, Forecasting, and Multinational Financial Management
assume a loan of $10,000 at the prime rate (currently 5.25%) with a 360-day year.
Interest must be paid monthly, and the principal is payable “on demand” if and
when the bank wants to end the loan. Such a loan is called a regular, or simple,
interest loan.
We begin by dividing the nominal interest rate (5.25% in this case) by 360 to get
the rate per day. The rate is expressed as a decimal fraction, not as a percentage:Simple interest rate per day! Nominal r____________ ate
Days in year
! 0.0525/360! 0.00014583333To! nd the monthly interest payment, the daily rate is multiplied by the amount of
the loan, then by the number of days during the payment period. For our illustrative
loan, the daily interest charge would be $1.458333333 and the total for a 30-day
month would be $43.75:Interest charge for month! (Rate per day)(Amount of loan)(Days in month)
! (0.00014583333)($10,000)(30 days)! $43.75The effective interest rate on a loan depends on how frequently interest
must be paid—the more frequently interest is paid, the higher the effective
rate. If interest is paid once a year, the nominal rate also will be the effective
rate. However, if interest must be paid monthly, the effective rate will be (1!
0.0525/12)^12 – 1 " 5.3782%.Calculating Banks’ Interest Charges: Add-On Interest
Banks and other lenders typically use add-on interest for automobiles and other
types of installment loans. The term add-on means that the interest is calculated
and then added to the amount borrowed to determine the loan’s face value. To
illustrate, suppose you borrow $10,000 on an add-on basis at a nominal rate of
7.25% to buy a car, with the loan to be repaid in 12 monthly installments. At a
7.25% add-on rate, you would make total interest payments of $10,000(0.0725) "
$725. However, since the loan is paid off in monthly installments, you would have
the use of the full $10,000 for only the! rst month; and the outstanding balance
would decline until, during the last month, only 1/12 of the original loan was still
outstanding. Thus, you would be paying $725 for the use of only about half the
loan’s face amount, as the average usable funds would be only about $5,000. There-
fore, we can calculate the approximate annual rate as 14.5%:15-7 Approximate annual rateAdd-on! __________________Interest paid
(Amount received)/2! _________$725
$10,000/2
! 14.5%The annual percentage rate (APR) the bank provides to the borrower would be
13.12%, and the true effective annual rate would be 13.94%. Both of those rates are
far higher than the nominal 7.25%.^21Regular, or Simple,
Interest
The situation when only
interest is paid monthly.Regular, or Simple,
Interest
The situation when only
interest is paid monthly.Add-On Interest
Interest that is calculated
and added to funds
received to determine the
face amount of an
installment loan.Add-On Interest
Interest that is calculated
and added to funds
received to determine the
face amount of an
installment loan.(^21) To! nd the annual percentage rate and the e# ective rate on an add-on loan, we! rst! nd the payment per
month, $10,725/12 " $893.75. With a! nancial calculator, enter N " 12, PV " 10000, PMT " #893.75, and FV " 0;
then press I/YR to obtain 1.093585%. This is a monthly rate; so multiply by 12 to get 13.12%, which is the APR the
bank would report to the borrower. The e# ective annual rate would be (1.010936)^12 # 1 " 13.94%, quite a bit
above the APR.