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+1 vote
asked Apr 3, 2018 in BUS 1003H - Introduction to Financial Risk by CHBMIL003 (150 points)

Question 5


 A loan of R80 000 is repayable over 10 years by monthly instalments in arrears . The repayments are calculated using an effective rate of interest of 8% per annum. Calculate the size of the first and last monthly instalments given that each payment after the first increases by 5% from its predecessor.


I have tried deducting the loan repayment amount(excluding interest) from the repayment amount i got of 958,...., which then gave me an answer of around 290, which i divided by 12, to get near to the answer. But this is incorrect, I would appreciate if someone were to help with the above question.



1 Answer

+1 vote
answered Apr 3, 2018 by kbunge (160 points)

The way I would approach this is to treat it like any other increasing annuities question:

The present value is R80000, since that is the amount we must pay back.

We know the number of monthly payments, we know the annual interest rate which we can use to calculate the monthly effective interest rate, and we know the growth factor. The only thing we don't know is the amount for the first payment in one months time. 

If you set up the equation of value, you should see that every payment after the first payment, is equal to the first payment multiplied by increasing powers of the growth factor. So, you can take out the common factor (the first payment), and solve for it.

If you have the value of the first payment, you can just solve for the last payment by multiplying the first payment by the growth factor with the appropriate exponent.

I hope this helps.