- Interest (I)
- Interest rate (r)
- Present value (P)
I = Prt
where I is the amount of interest, P is the principal (amount of moneyborrowed), r is the interest rate (per year), and t is the time (expressed inyears). 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 initialprincipal and the interest due on it.
Interest (I)
The most basic question is of the form, if you borrow $250 for three months at6% (=.06) simple interest, how much interest must you pay? The answer is easilycalculated from I = Prt as I = $250×.06 ×.25 = $3.75. Onecould 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 canrearrange I = Prt to r = I/(Pt) to get r = $1/($100×(2/52)) = .26 (or26%)One can of course solve the equation for P or t, but these are generally knownquantities.
Exercise: If Sally borrows $300 for six weeks at 8% interest, how much interestmust she pay? What is the total amount she must repay?
If John borrows $400 and has to repay $412 in two months, what interestrate 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 toknow how much he can borrow now, for example, if one is taking a loan untilpayday. 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%, theprincipal 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, howmuch interest must one pay? What is the total amount one mustrepay?
If one borrows $500 for six months and has to repay $600, what is the interestrate?
If Jan is going to receive $10,000 in four weeks, how much can she borrow now at6% simple interest?
Reflection:
Challenge:
May2003
