Chapter 8 Loans
264
Single-Payment Loans
There are many ways that money can be borrowed and repaid. The simplest
is a single-payment loan, which is a loan that is repaid in one payment with
interest. The principal is the original sum of money borrowed. The term is the
length of time that the money will be borrowed. At the end of the term, the loan
must be repaid.
As with the other examples of interest in this text, loan interest is also
expressed as an annual rate. In a single-payment loan, the interest is paid at the
end of the term, along with the principal repayment. If money is borrowed for
exactly one year, the formula for simple interest can be used. In this formula,
t = 1, because there is only one payment period in a single payment loan. If, for
example, the annual rate is 10%, the interest due at the end of the year is 10% of
the principal. For a single-payment loan, the following formula can be used to
calculate interest:
I = Prt
Example 8-1A
See It
Martha borrowed $1,600 from her parents. They agreed that at the end of
one year, Martha would repay the entire amount plus 8.5% interest. How much
interest will Martha owe her parents?
Strategy
Use the formula:
I = Prt
Solution
Step 1: Convert the annual interest rate to a decimal by moving the decimal two
places to the left.
8.5% → 0.085
Step 2: Determine the annual interest amount. Multiply the principal by the
annual interest rate.
interest owed = principal × rate × term
interest owed = $1,600 × 0.085 × 1
interest owed = $136
Check It
Jerome borrowed $2,500 from his grandparents to pay his fall semester
college tuition payment. They agreed that at the end of one year, Jerome would
repay the entire amount plus 4.75% interest. How much interest will Jerome owe
his grandparents?
fyi
In the formula for simple
interest: I is for interest
paid; P is for principal; r
is interest rate; and t is
term.