Value Worksheet With Answer Key Page 2
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1
2
3
4
5
6
7
8Reflecting
In what ways is calculating the amount, or future value, of an annuity
E.
the same as calculating the amount, or future value, of a single deposit?
In what ways is it different?
A 5 53500(1 1 0.03)
4
5
Why can’t the formula
be used to calculate
F.
the amount of Jessica’s annuity?
Create an expression that represents the sum of the amounts, or future
G.
R(1 1 i)
n
value, of the six deposits. Use expressions of the form
,
where
• R is the regular deposit or payment, in dollars
• i is the interest rate per compounding period, expressed as a decimal
• for each deposit, n is the number of compounding periods
APPLY the Math
1
Selecting a strategy to calculate the amount of an annuity
EXAMPLE
Steve makes deposits of $300 semi-annually into an account that pays 4%/a interest
compounded semi-annually.
a) How much money will be in the account after 5 years?
b) How much interest will Steve have earned over the 5-year term?
Marta’s Solution: Using a Timeline
Year
0
1
2
3
4
5
Future value
a)
The amount of the regular payment
R 5 $300.
is
Deposit
$300
$300
$300
$300
$300
$300
$300
$300 $300
$300
300
The annual interest rate is 4%, or
1
300(1.02)
2
300(1.02)
0.04, so the semi-annual interest rate
3
300(1.02)
i 5 0.02.
is
4
300(1.02)
5
300(1.02)
I created a timeline to organize the
6
300(1.02)
7
300(1.02)
calculations of the future value of
8
300(1.02)
each deposit.
9
300(1.02)
Future value of Steve’s annuity
The total of the individual future
Total amount
values is the amount in Steve’s
5 300 1 300(1.02)
1 300(1.02)
1 ... 1 300(1.02)
1
2
9
account at the end of year 5.
5 300 1 306 1 312.12 1 318.36 1 324.73
1 331.22 1 337.85 1 344.61 1 351.50 1 358.53
5 3284.92
10 3 $300.
The total of the deposits is
Steve will earn a total of $3284.92.
The difference between the deposits
3284.92 2 (10 3 300) 5 284.92
b)
and the total amount is the interest
earned.
$284.92 of the amount is interest earned.
494
Chapter 8
NEL
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