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# Interest compounded quartely Watch

1. Hi,
One of your fellow students saves up money for a used car by depositing a fixed amount in the bank every 1st day of the quarter for 5 years. The bank pays an interest of 6 % per annum compounded quarterly. Your fellow student wishes to have 30,000 DKK at his disposal at the end of the 5 years.
Calculate the necessary quarterly payment.
APR=100 ((1+(r/n)/100)^n-1) e.i. APR=100((1+(6/4)/100)^4-1)=6,136355062
What next, where I need to use 5 years?
2. I'm not sure how you're doing it, but this is how I would do it.

Investments receive interest from the bank, compounded quarterly.
The annual interest rate is 6%, so the quarterly interest rate is 1.5%.
The interest is compounded so the return on a Payment P over t quarterly terms is given by,

where a = 0.015

At the beginning of the 5 year period, the student makes a quarterly payment of P. The return on that payment is given by

and for the second payment, the return is,

then,

Can you see how this is going?

You've got to sum up all the returns to get 30,000 DKK

Can you do it now?

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Updated: December 2, 2010
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