A sum of money is borrowed, for a ten-year term, as a depreciating balance annuity, at a fixed interest rate of 15% per annum. Repayments are to be made on a monthly basis.

The borrower decides, from payment one, to increase the monthly repayment by ten percent, rounded off upwards to the nearest Rand.

Determine,

(a) the difference in the final total repayment made by the borrower, as a result of increasing the monthly repayments,

(b) how many repayments have to be made for the total sum repaid, up to that point, to equal, or just exceed, the outstanding balance of the depreciating annuity, 

 

(c) determine the number of monthly repayments that have to be made for the capital redemption portion of the monthly repayment to equal, or just exceed, 

 

(i) half the interest portion of the monthly repayment,

(ii) the interest portion of the monthly repayment,

(iii) twice the interest portion of the monthly repayments,

(d) Provide, under a cover page, with a content page, introduction, method/technique, problem statement, graphs, and conclusion a neat, fully annotated, large format graph,on which are shown

 

(i) balances at any time for  minimum monthly repayments and  increased monthly repayments  

(ii) total amount repaid at any time for minimum monthly repayments and increased monthly repayments 

 

(iii) difference in the repayment period

(e) determine the repayment period that will make the total sum repaid equal to two and a half times the sum borrowed.