Question 1088676: nikki deposits $200 at the end of every month in an account that pays 3.5%/a compounded quarterly for 2 years for her college. Calculate her future value
Answer by mathmate(429)   (Show Source):
You can put this solution on YOUR website! Question:
nikki deposits $200 at the end of every month in an account that pays 3.5%/a compounded quarterly for 2 years for her college. Calculate her future value
Solution:
Here the compounding is every three months, while the payment is every month.
Therefore she get paid simple interest every third month, and then compounded, 8 times in two years.
Simple interest
=200*.035/12(0+1+2 months) [ she pays at the end of the month ]
=$1.75
So every three months, she has effectively contributed $601.75.
A=quarterly amount = $601.75
i=interest per quarter = 0.035/4
n=number of periods (months) = 2*4=8
The future amount
F=A((1+i)^8-1)/(i)
=601.75*((1+0.035/4)^8-1)/(0.035/4)
=4964.04
She collects $4964.04 at the end of two years.
Just for comparison, if the deposits were compounded every month, the final amount would have been
F=200((1+0.035/12)^24-1)/(0.035/24)
=4964.50, a mere difference of 46 cents if compounded monthly.
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