Apps. and Interpretation for IBDP Maths Ebook 1 | Page 87

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Paper 1 – Equivalent Rates
Example
360000 USD is invested for 6 years at a nominal annual interest rate of 4%, compounded
yearly.
(a) Find the value of P , the amount of money after 6 years, give the answer correct
to the nearest USD.
[3]
(b) 360000 USD is invested for 6 years at a nominal annual interest rate of r % ,
compounded half-yearly. The amount of money after 6 years is P . Find the value
of r .
[3]
Solution
(a)
(b)
6
� 4 �
P �360000 �1�
�
� 100 �
(M1)(A1) for substitution
P � 455514.8467
P � 455515 USD A1 N3
By TVM Solver :
N�
6
I% � 4
PV ��360000
PMT � 0
(M1)(A1) for correct values
FV � ?
P / Y �1
C / Y �1
PMT : END
P � 455515 USD A1 N3
[3]
(2)(6)
� r �
360000 �1�
� �455514.8467
� (100)(2) �
12
� r �
360000 �1� � �455514.8467 �0
� 200 �
By considering the graph of
� r �
y �360000 �1� � �455514.8467
,
� 200 �
r � 3.9607805 .
12
(M1)(A1) for correct equation
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