If you invest money at a given interest rate, what willbe the future value of your investment?An investment of $1 earning an interest rate of r willincrease in value each period by the factor (1 + r). After tperiods its value will grow to $(1 + r)t. This is the futurevalue of the $1 investment with compound interest.
What is the present value of a cash flow to be receivedin the future?The present value of a future cash payment is the amountthat you would need to invest today to match that futurepayment. To calculate present value, we divide the cashpayment by (1 + r)t or, equivalently, multiply by the discountfactor 1/(1 + r)t. The discount factor measuresthe value today of $1 received in period t.
How can we calculate present and future values ofstreams of cash payments?A level stream of cash payments that continues indefinitelyis known as a perpetuity; one that continues for alimited number of years is called an annuity. The presentvalue of a stream of cash flows is simply the sum of thepresent value of each cash flow. Similarly, the future valueof an annuity is the sum of the future value of each individualcash flow. Shortcut formulas make the calculationsfor perpetuities and annuities easy. Variations of theseformulas make it easy to calculate the present value ofcash flows growing at a constant rate.
What is the difference between real and nominal cashflows and real and nominal interest rates?A dollar is a dollar but the amount of goods that a dollarcan buy is eroded by inflation. If prices double, the realvalue of a dollar halves. Financial managers and economistsoften find it helpful to re-express future cash flowsin terms of real dollars—that is, dollars of constant purchasingpower.Be careful to distinguish the nominal interest rate andthe real interest rate—that is, the rate at which the realvalue of the investment grows. Discount nominal cashflows (that is, cash flows measured in current dollars) atnominal interest rates. Discount real cash flows (cashflows measured in constant dollars) at real interest rates.Never mix and match nominal and real.
How should we compare interest rates quoted over differenttime intervals—for example, monthly versusannual rates?Interest rates for short time periods are often quoted asannual rates by multiplying the per-period rate by thenumber of periods in a year. These annual percentagerates (APRs) do not recognize the effect of compoundinterest, that is, they annualize, assuming simple interest.The effective annual rate (EAR) annualizes using compoundinterest. It equals the rate of interest per periodcompounded for the number of periods in a year.
