Question

Suppose you want to have $500,000 for retirement in 20 years. Your account earns 5% interest. How much would you need to deposit in the account each month?

Answer 1

An ordinary annuity is a series of equal periodic payments made at the end of each period, with interest compounding at the end of each period. Annuity problems can be solved using annuity tables, formulas, spreadsheet functions, or a financial calculator. The calculator is simplest once you understand annuities and compound interest. You are given some information and you have to solve for an unknown variable. There are four of five variables that have to be input into the formula or spreadsheet or calculator. The formula for calculating equal periodic payments is:-

Where,

PV = present value, a sum with which the annuity starts the will pay future rents (period payments).

FV = future value, a sum that will accumulate from the periodic rents and the interest earned.

PMT =the amount of periodic rent

N = the number of rents

i% = the percentage interest compounding over N periods.

In this problem you have PV, FV. N, and i% and you must solve for PMT.

Interest is always expressed in annual terms. If the rents are monthly, the interest rate has to be converted to monthly interest also.

PV = 0

PMT =?

N = 20 yrs. * 12 = 240

i% = 5% / 12 = .4167%

FV = 500,000

By substituting the values in the equation we get,

the amount of equal payment to be deposited in the account each month is $1,216.38