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
