Suppose you have decided to put $200 at the beginning of every month in a savings account that credits interest at the annual rate of 6%, but compounds it monthly. Find the amount in this account after 30 years.

 Suppose you have decided to put $200 at the beginning of every month in a savings account that credits interest at the annual rate of 6%, but compounds it monthly. Find the amount in this account after 30 years.

Answer

monthly rate of interest  = 6%/12 = 0.005

Number of months = 30 x 12 = 360

S = 200 (1.005)^360 + 200 (1.005)^359+ …….+200 (1.005)

Here , a=200 (1.005)^360 and x = 1/1.005

 

FV = 200 (1.005)^360 [1-(1/1/1.005^360)] / 1-1/1.005

Now, 1/1.005^360 = 1.005^-360 (Simple math)

FV = 200 (1.005)^360 [1-1.005^-360]/1-1.005^-1

FV = 201,907.52