Apps. and Interpretation for IBDP Maths Ebook 1 | Page 93

Exercise 26
1. An annuity fund is created and it requires regular payments at the beginning of every year
for 20 years. The value of the fund at the end of 20 years is $60000 and the interest is
earned 7.5% per year.
(a) Find the value of the regular payment per year.
[3]
(b) If the value of the regular payment per year is increased by $500, find the number
of years required for the investment.
[3]
2. Simon wants to accumulate an amount of money in an education fund at the end of 10
years. He deposits $1000 at the end of each month in the first five years, and deposits
$1500 at the end of each month in the last five years. The interest is earned 3% per year.
(a)
(b)
Find the value of the investment after five years.
Find the value of the investment after ten years.
3. Teddy wants to accumulate an amount of money in an investment plans. He deposits
$300 at the end of March, June, September and December every year. The interest is
earned 5% per year.
(a) Let P be the value of the investment after fifteen years. Find the value of P .
[3]
(b) If Teddy wants to adjust the amount of deposit such that the value of the
investment after thirty years is 3.5P , find the new amount of deposit.
[3]
4. Consider the following table of the payments of the annuities X and Y , at the beginning
of each month:
[3]
[3]
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Annuity X Annuity Y
1st to 8th year 100 p
9th to 16th year 200 p
It is given that the values of the investment after sixteen years for both annuities are the
same. The interest is earned 2.9% per year for both annuities.
(a) Find the value of the investment after eight years for annuity X .
(b) Find the value of the investment after sixteen years for annuity X .
(c) Hence, find the value of p .
[3]
[3]
[2]
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