How to Calculate Annuity and Flat Interest Formulas

A flat-interest loan is a financial transaction in which one party loans another party a sum of money, which is paid back with interest at the end of a specified number of periods. On the other hand, an annuity is a loan that is paid back with interest over time, so that the lender receives money each period, rather than simply a lump sum at the end. Learn how to determine the end worth of each type of loan.

Things You'll Need

• Calculator

Instructions

Flat-Interest Loan

1. The future value of a flat-interest loan is calculated by the formula D = L(1+(i*N)], where D = the amount of money due at the completion of the loan, L = the amount of money loaned, i = the interest rate per period, and N = the total number of periods.

2. Multiply the interest rate (i) times the number of periods (N) and then add 1. Call this number "a."
   [(i)(N)+1] = a

3. Multiply "a" times the amount of money borrowed (L). The resulting number is the money owed to the lender, or the future value of the loan.
   (a)(L) = D

Annuity

1. The future value of an annuity is calculated by the formula F = P[((1 + i)^N -1)/i], where F = the future value of the annuity, P = the payments per period, i = the interest rate per period, and N = the total number of periods.

2. Add 1 to the interest rate and call this number "y." For example, if the interest rate is 5 percent, then y = 1.05.
   (1+i) = y

3. Take y to the N power, where N is the number of periods. This step will require a calculator with a y^x function, or the manual calculation of y times itself N times. We'll call this new number "x."
   (y)^N = x

4. Subtract 1 from x and then divide by the interest rate (i). Call this number "z."
   (x-1)/i = z

5. Multiply z times the amount of each payment (P). The resulting number is the future value of the annuity.
   (P)(z) = F