You have decided to put $130 in a savings account at the end of each month. The savings account credits interest monthly, at the annual rate of 6%. How much money is in your account after 6 years?

You have decided to put $130 in a savings account at the end of each month. The savings account credits interest monthly, at the annual rate of 6%. How much money is in your account after 6 years?

Solution

monthly rate of interest  = 6%/12 = 0.005

Number of months = 6 x 12 = 72

Deposit made at the end of each month so, Number of years = 72-1 = 71

S = 130 (1.005)^71 + 130 (1.005)^70+ …….+130 (1.005)

Here , a=130 (1.005)^71 and x = 1/1.005

 

FV = 130+[130 (1.005)^71 [1-(1/1/1.005^71)] / 1-1/1.005 ]

Now, 1/1.005^71 = 1.005^-71 (Simple math)

FV = 130+130 (1.005)^71 [1-1.005^-71]/1-1.005^-1

FV = 11,233.15