Section 1.2
The Term of a Loan
Copyright © 2011 Department of
Mathematics, Penn State University
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FORMULA 1
The Simple Interest Formula
I = PRT
where
I = simple interest
P = principal
R = interest rate (expressed as a decimal)
T = term (expressed in years)
MUST ADJUST T SO THAT IT IS IN TERMS OF YEARS!
Copyright © 2011 Department of
Mathematics, Penn State University
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Term of a Loan (Expressed in years)
• If a problem expresses the term in months it needs to be
converted to years by dividing by 12.
T = months/12
• If a problem expresses the term in days, it needs to be
converted to years by dividing by 360, 365 or 366.
Exact method – interest is calculated on the basis of the
actual number of days in the year (365 or 366)
T= days/365 or days/366
Simplified Exact method - interest is calculated on the
basis of the of 365 days in the year
T= days/365 (Use this if no method is specified)
Banker’s Rule - interest is calculated on the basis of the
of 360 days in the year (30 days per month)
T= days/360
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Mathematics, Penn State University
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Term of a Loan (Expressed in years)
• If a problem expresses the term in weeks it needs to be
converted to years by dividing by 52. This situation is not
used very often.
T = weeks/52
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Mathematics, Penn State University
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Example 2 (Months)
• If Sara borrows $5,000 for 6 months at 9% simple interest, how
much will she need to pay back?
• Solution
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Mathematics, Penn State University
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Example 3 (Days – All Methods)
• Calculate the simple interest due on a 120-day loan of $1,000 at
8.6% simple interest in three different ways: assuming there are
365, 366, or 365.25 days in the year.
• Solution
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Mathematics, Penn State University
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Example 4 (Days – Simplified Exact Method)
• Nick deposited $1,600 in a credit union CD with a term of 90
days and a simple interest rate of 4.72%. Using the simplified
exact method, find the value of his account at the end of its
term.
• Solution
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Mathematics, Penn State University
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Example 5 (Days – Banker’s Rule)
• Using Banker’s Rule, calculate the interest due on a 120-day
loan of $10,000 at 8.6% simple interest.
• Solution
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Mathematics, Penn State University
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Example 6 (Weeks)
• Bridget borrows $2,000 for 13 weeks at 6% simple interest.
Find the total amount of interest she will pay.
• Solution
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Mathematics, Penn State University
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Application Example
• A volunteer ambulance company was conducting a fund drive
to buy a new ambulance when the old one broke down
entirely and had to be replaced. The fund drive was going
well, but the company had not yet reached it goal, and so
could only pay for part of the cost of the new ambulance.
They financed the remaining $22,453 with a 5-month loan at
8.23% simple interest. Find the amount they will need to raise
to pay off this loan.
• Solution
Copyright © 2011 Department of
Mathematics, Penn State University
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