Value Worksheet With Answer Key Page 4
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8If technology is not available to help you calculate the future value of an
annuity, you can do so using a formula.
2
Using a formula to determine the future
EXAMPLE
value of an annuity
Jay deposits $1500 every 3 months for 2 years into a savings account that earns
10%/a compounded quarterly. How much money will have accumulated at the
end of 2 years?
Measha’s Solution
R 3 (1 1 i)
2 14
n
I wrote the formula for calculating the future
A 5
i
value of an annuity, where
• A is the amount, or future value, in dollars
R 5 $1500
• R is the regular deposit, or payment, in dollars
i 5 10% 4 4
• i is the interest rate per compounding period,
expressed as a decimal
5 2.5% 5
0.025
• n is the total number of deposits
n 5 2 3 4 5 8
The interest rate is 10% compounded quarterly.
15003(1 1 0.025)
2 14
8
To determine i, I divided it by 4.
A 5
0.025
I multiplied the number of years by 4 to
5 13 104.17
determine the number of compounding
periods.
Jay will have $13 107.17 at
the end of 2 years.
3
Selecting a strategy to calculate the
EXAMPLE
regular payment
An investor wants to retire in 25 years with $1 000 000 in savings. Her current
investments are earning, on average, 12%/a compounded annually.
a) What regular annual deposit must she make to have the required amount
at retirement?
b) How much of the $1 000 000 is interest earned?
Andrea’s Solution: Using a Formula
R 3 (1 1 i)
2 14
n
I wrote the formula for calculating
A 5
a)
the future value of an annuity.
i
R 3(1 1 0.12)
2 14
25
A 5 $1 000 000.
The future value is
1 000 000 5
0.12
i 5 0.12.
The annual interest rate is
Regular deposits are made every year,
so n 5 25.
496
Chapter 8
NEL
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