Apps. and Interpretation for IBDP Maths Ebook 1 | Page 92

Your Practice Set – Applications and Interpretation for IBDP Mathematics
26
Paper 1 – Annuities
Example
Kevin is going to create an annuity fund which will pay him a monthly allowance of 2000
USD for 40 years after he is retired. In the fund, interest is earned 6% per year,
compounded yearly.
(a)
(b)
Find the value of the annuity fund that has to be saved, giving the answer correct
to the nearest USD.
[3]
Find the amount of payment needed per year if Kevin wants to save his money in
his fund for 30 years.
[3]
Solution
82
(a)
(b)
By TVM Solver:
N �40�12
I% � 6
PV � ?
PMT � 2000
FV � 0
(M1)(A1) for correct values
P / Y � 12
C / Y � 1
PMT : END
PV �� 370397.2097
Thus, the value of the annuity fund that has to be
saved is 370937 USD. A1 N3
[3]
By TVM Solver:
N � 30
I% � 6
PV � 0
PMT � ?
FV � 370937.2097
(M1)(A1) for correct values
P / Y �1
C / Y �1
PMT : END
PMT �� 4691.951934
Thus, the amount of payment needed per year is
4690 USD. A1 N3
[3]
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