# How to Calculate Annuity and Flat Interest Formulas

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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. These steps will help you determine the end worth of each type of loan.

## Flat Interest Loan

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.

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

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

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.

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

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

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

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