Apps. and Interpretation for IBDP Maths Ebook 1 | Page 99

4. Daniel is a financial analyst and he is investigating the differences of various
amortization schedules when some of the factors are changed.
Firstly, he is investigating the differences between the amortization schedules with
payments at the beginning of each year and at the end of each year, by considering the
following two versions:
Version 1: A total of 20 equal yearly payments of $R
1
have to be paid at the beginning of
each year
Version 2: A total of 20 equal yearly payments of $R
2
have to be paid at the end of each
year
Both versions are designed for a loan of $50000, with a nominal annual interest rate of
2%.
(a) (i) Find the value of R
1.
(ii) Find the value of R
2
.
(iii) Interpret the meaning of $20( R2� R1)
.
(iv)
State which version will have the smaller total amount to be paid.
[8]
9
In addition, he is also investigating the differences between the amortization schedules
with yearly payments and monthly payments, by considering the following additional
version:
Version 3: A total of 240 equal monthly payments of $R
3
have to be paid at the end of
each month
The version 3 is designed for a loan of $50000, with a nominal annual interest rate of 2%.
(b) (i) Find the value of R
3
.
(ii) Interpret the meaning of $(240R3
� 50000) .
(iii)
By comparing the version 2 and the version 3, determine which version
will have the smaller total amount to be paid. Justify the answer.
[7]
89
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