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    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?
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    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,

    R = P(1+a)^t

    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

    R_1=P(1+a)^{20}

    and for the second payment, the return is,

    R_2=P(1+a)^{19}

    then,

    R_3=P(1+a)^{18}

    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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