Apps. and Interpretation for IBDP Maths Ebook 1 | Page 98

Your Practice Set – Applications and Interpretation for IBDP Mathematics
3. Clement works in a bank and he is designing the structure of an amortization schedule for
customers. He suggests the version 1 of the amortization schedule for a loan of $10000,
with a nominal annual interest rate of 2%:
Version 1: A total of 120 equal monthly payments of $R have to be paid at the end of
each month in a ten-year period
(a)
Find
(i) the value of R ,
(ii)
the amount of interest paid.
Clement then makes some amendments in the version 1, such that the version 2 of the
amortization schedule is as follows:
[6]
Version 2: A total of 60 equal monthly payments of $R have to be paid at the end of
each month in the first five years, then the amount of monthly payments of $( R � 60)
have to be paid at the end of each month, until the loan is fully repaid
(b) (i) Find the number of months to repay the loan, rounding up the answer
correct to the nearest month.
(ii)
Find the amount of interest paid.
(iii) Explain the reason why the version 2 of the amortization schedule is more
favourable to customers than the version 1.
[9]
Clement later makes the final amendments in the version 2, such that the version 3 of the
amortization schedule is as follows:
Version 3: A monthly payment of $1.5R has to be paid at the end of each month until the
loan is fully repaid
(c) (i) Find the number of months to repay the loan, rounding up the answer
correct to the nearest month.
(ii)
Hence, write down the difference of the number of months required to
repay the loan between the version 2 and the version 3.
[4]
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