# Simple interest

Simple interest is the form of interest used for short term loans, such as one receives at pawnshops or from loan sharks. It is governed by the formula:

I = Prt

where I is the amount of interest, P is the principal (amount of money borrowed), r is the interest rate (per year), and t is the time (expressed in years). The formula can also be expressed as:

A = P + I = P(1 + rt)

where A is the amount to be repaid, one must repay both the initial principal and the interest due on it.

## Interest (I)

The most basic question is of the form, if you borrow \$250 for three months at 6% (=.06) simple interest, how much interest must you pay? The answer is easily calculated from I = Prt as I = \$250×.06 ×.25 = \$3.75. One could also ask how much one must repay, which is \$250 + \$3.75 = \$253.75.

## Interest rate (r)

Another question is, what interest are you paying? For example, If you borrow \$100 for two weeks, and pay \$1 interest, what is the interest rate? One can rearrange I = Prt to r = I/(Pt) to get r = \$1/(\$100×(2/52)) = .26 (or 26%)

One can of course solve the equation for P or t, but these are generally known quantities.

Exercise: If Sally borrows \$300 for six weeks at 8% interest, how much interest must she pay? What is the total amount she must repay?
If John borrows \$400 and has to repay \$412 in two months, what interest rate is he being charged?

## Present value (P)

The formula A = P(1 + rt) gives the future value, A, of the principal now (present value). One may know how much he can repay in two weeks, and want to know how much he can borrow now, for example, if one is taking a loan until payday. A = P(1 + rt) can be rewritten as:

P = A/(1 + rt)

If one is going to be paid \$375 in two weeks, and the interest rate is 12%, the principal one can borrow now is P = \$375/(1 + .12×(2/52)) = \$373.28.

One can of course also solve for the interest rate or the time.

CompetencyIf one borrows \$400 for eight months at 18% interest, how much interest must one pay? What is the total amount one must repay?
If one borrows \$500 for six months and has to repay \$600, what is the interest rate?
If Jan is going to receive \$10,000 in four weeks, how much can she borrow now at 6% simple interest?

Reflection:

Challenge:

May2003

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campbell@math.uni.edu