# How to Calculate Implied Interest Rate

Implied interest rates are used in currency, commodities and futures investments. The implied interest rate represents the difference between the spot rate and future or forward price for the investment. The spot rate is the current, real-time price of the investment. The forward or future price represents its expected spot price at some future time. To calculate the implied interest rate, find the ratio of the forward price over the spot price. Raise that ratio to the power of 1 divided by the length of time until expiration of the forward contract, then subtract 1. The formula is:

i = (forward price/spot price)^(1/t) - 1

where t = length of the forward contract

## Implied Interest Rate for Commodities

If the spot rate for a barrel of oil is \$98 and a futures contract for a barrel of oil in one year is \$104, the implied interest rate is:

i = (104/98) -1 i = 6.1 percent

Divide the futures price of \$104 by the spot price of \$98. Since this is a one-year contract, the ratio is simply raised to the power of 1. Subtract 1 from the ratio and compute the implied interest rate of 6.1 percent.

## Implied Interest Rate for Stocks

If a stock is currently trading at \$55 and there is a two-year forward contract trading at \$58, the implied interest rate is:

i = (58/55) ^(1/2) - 1 i = 2.7 percent

Divide the forward price of \$58 by the spot price of \$55. Since this is a two-year futures contract, raise the ratio to the power of 1/2. Subtract 1 from the answer to find the implied interest rate is 2.7 percent.

## Implied Interest Rate for Currencies

If the spot rate for the euro is \$1.10 and the one-year futures price for the euro is \$1.15, the implied interest rate is calculated as:

i = (1.15/1.10) - 1 i = 4.5 percent

Calculate the ratio of the forward price over the spot price by dividing 1.15 by 1.1. Since this is a one-year forward contract, the ratio is simply raised to the power of 1. Subtracting 1 from the ratio of the forward price over the spot price results in an implied interest rate of 4.5 percent.

## Using Implied Interest Rates for Investment Decisions

Implied interest rates are useful to investors because the implied interest rate in the options markets should reflect other short-term interest rates. The implied interest rate gives investors a way to compare return across investments and evaluate the risk and return characteristics of that particular security. An implied interest rate can be calculated for any type of security that also has an option or futures contract.

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