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?

 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?

Solution

Sn= down payment =25,000 , interest monthly = 0.75% = 0.0075

25,000 = 200(1.0075)^n+ 200(1.0075)^n−1 + ... + 100(1.0075)

25,000 = 200(1.0075)^n+ 200(1.0075)^n−1 + ... +200(1.0075)

Here a = 200(1.0075)^n, x =1/1.0075, Sn= 25,000

25,000 = 200(1.0075)^n [1-(1/1.0075^n)]/1-1/1.0075

25,000 = 200(1.0075)^n -200/0.007444169

25,000 x 0.007444169 = 200(1.0075)^n -200

186.10 = 200(1.0075)^n -200

186.10 +200 =  200(1.0075)^n

386.10 =200(1.0075)^n

386.10 /200 = (1.0075)^n

1.930521 = (1.0075)^n

Taking ln both sides, we get

Ln(1.930521) = n ln(1.0075)

N = Ln(1.930521)/ ln(1.0075)

N = 88 months