Present value, interest rate and future value all relate closely to the time value of money. While the interest rate – a percentage of the present value, also called the principal or starting balance – is often a known variable in solving interest rate problems, this is not always the case. Knowing how to calculate an interest rate using present and future value can be helpful in valuing short-term discount bond investments such as Treasury bills or to determine the current market interest rate during the time you hold long-term discount bonds
Calculate Interest Rate of a Short-Term Discount Bond
Identify variables you need to calculate the interest rate on a discount. These include the present value or initial purchase price, the number of days to maturity (which in the case of a T-bill is 30, 91 or 182 days) and the future value, or face value, for which you will redeem the bond when it matures.
Evaluate the equation for calculating the interest rate or yield of the bond to understand how the calculation works. Set up the equation using the formula:
Interest rate = ((future value - present value) / future value) * (360 / days to maturity)
Insert bond information and complete the calculation. If you have a bond that costs $5,659.30 today, matures in 182 days and has a future value of $6,000, the interest rate is 11.23 percent:
((6000 – 5,659.30) / 6000) * (360 / 182) = .0567833 * 1.9780219 = .1123
Calculate Current Market Interest Rate
Identify variables you need to calculate the current market interest rate. For example, in the case of a zero coupon bond – a type of discount bond in which the purchase often varies and interest accrues annually – variables include present value, the coupon rate and the future value of the bond. Present value is the amount for which a bond is currently selling rather than its price at the time of purchase; the coupon rate is the rate of interest the bond pays each year; and future value is the face value of the bond.
Evaluate the equation for calculating the current market interest rate. Set up the equation using the formula:
Current Market Interest Rate = Annual Interest Payment (future value * coupon rate) / present value
Insert bond information and complete the calculation. If you have a bond that has a face value of $20,000, a coupon rate of 5 percent and a present value (current purchase price) of $6,757, the current market interest rate is 14.8 percent. To illustrate how the current market interest rate can fluctuate, if the purchase price of the bond rises to $8,000, the current market interest falls to 12.5 percent.
Annual Interest Payment = (20,000 * .05) = $1,000 Current Market Interest Rate = 1000/6757 = .14499 or Current Market Interest Rate = 1000/8000 = .125