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.
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?
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
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?