# How to Calculate the Equivalent Interest for an Investment Return

When interest on your investments is paid more frequently than once a year, you may in fact be earning a higher rate of interest on your savings than the posted rate given to you by your financial institution. You may wish to calculate this earned annual interest rate to make comparisons between all your investments. You may also wish to calculate the interest rate earned on a given amount of interest you received in a year in order to determine the performance of your investments.

## Compounding Frequency

An interest rate given to you as compounding with a frequency other than annual can easily be converted to an annual equivalent rate. Use the formula AI = (1+i/n)^n -1, where AI is your annual equivalent interest rate, i is the posted interest rate on your investment and n is the frequency of compounding. A rate of 12 percent compounding monthly, for example, will have an annual equivalent interest rate of (1+0.12/12)^12 - 1 = 1.01^12 - 1 = 12.6825 percent. Your annual equivalent interest rate is higher than 12 percent due to the monthly compounding.

## Interest Credits

If you receive a certain amount of interest at the end of the year for a given investment, you may determine its equivalent interest rate by using the formula: i = Int / C, where Int is the amount of interest received and C is the capital amount of your investment. If you invested \$1,000 and received an interest payment of \$50 at the end of the year, your annual equivalent interest rate would be \$50 / \$1,000 = 5 percent.

## Bond Yield

Use the same approach if you wish to determine the annual equivalent yield, or the yield to maturity, on a bond. Use the formula Y = (1+C/PV)^n - 1, where C is the coupons, or interest paid, PV is the bond's par value, or purchase price, and n is the frequency of the coupon payments. A \$1,000 par value bond with semi-annual coupons of \$30 will have a yield to maturity of (1 + \$30/\$1,000)^2 - 1 = 1.03^2 -1 = 6.09 percent.

## IRR - Internal Rate of Return

Sometimes you may have a stream of investment returns deriving from the investment of a single capital outlay. The Internal Rate of Return is a measure that determines the annual equivalent interest rate for that stream of payments in relation to the capital outlay. Basically, the IRR is the interest rate at which the present value of your stream of payments equals the initial capital outlay. Assume you invested \$10,000 in a project and projected returns of \$3,000 next year, \$4,000 in year 2, \$4,500 in year 3 and \$6,000 in year 4. The internal rate of return is the annual interest discount factor at which the present value of the cash flows equals \$10,000. Using an online calculator you can figure out that the IRR in this example is 23.6 percent.