Question

Interest

Interest
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Exercise
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You borrow $3600 for 250 days at 8%. How much interest will you have to pay if the rate
is calculated using exact interest? Using ordinary interest?
Total exact interest
Total ordinary interest
SUBMIT

Answer 1

• exact: $197.26
• ordinary: $200

Explanation:

The amount of interest is computed using the formula ...

I = Prt

where P is the principal borrowed, r is the annual interest rate, and t is the number of years.

When the loan is for less than a whole year, the number of days is converted to years using a value for the number of days in a year. For "exact" interest, that number is 365 days per year. For "ordinary" interest, a year is considered to be 360 days. The fraction of a year is the number of days divided by the number of days per year.

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If d is the number of days per year, then the above formula with the given values filled in looks like ...

I = 3600×0.08×(250/d) . . . . for d = 365 or 360 (exact or ordinary interest)

For exact interest:

I = $3600×0.08×250/365 ≈ $197.26 . . . . total exact interest

For ordinary interest:

I = $3600×0.08×250/360 = $200.00 . . . . total ordinary interest

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Additional comment

In the attached calculator display, we used a matrix to represent days per year. That way, we could do both calculations at once without having to re-enter the numbers.