Question

Suppose you want to accumulate $25,000 as down payment on a house and the best you can do is to put aside $200 a month. If you deposit this amount at the beginning of each month in an account that credits 0.75% interest monthly, how long will it take you to attain your goal?

Answer 1

It will take 88.2 months to accumulate the amount

Explanation:

Given;

Future value of money, FV = $25,000

investment per compound period, P = $200

interest rate, i = 0.75% x 12 = 9%

The number of monthly installments required to amount to FV is given by;

`n = (ln(FVi +cp)-ln(cp))/(ln(c+i)-ln(c))\\\\ n = (ln(25000*0.09 +200*12)-ln(200*12))/(ln(12+0.09)-ln(12))\\\\n = (8.4446 -7.7832)/(2.4924-2.4849)\\\\n = 88.2 \ months`

Therefore, it will take 88.2 months to accumulate the amount.