Value Worksheet With Answer Key Page 6
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8In Summary
Key Ideas
• Since an annuity is a series of equal deposits made at regular intervals, the
amount, or future value, can be found by determining the sum of all the future
values for each regular payment.
• The amount, or future value, of an annuity is the sum of all deposits and the
accumulated interest and can be found with the formula
R3(1 1 i)
2 14
n
A 5
i
where
A is the amount, or future value, in dollars
•
R is the regular deposit, or payment, in dollars
•
i is the interest rate per compounding period, expressed as a decimal
•
n is the total number of deposits
•
Need to Know
• Problems involving annuities can be solved with a formula, spreadsheet
software, or financial software such as the TVM Solver.
• When the TVM Solver is used to solve problems that involve regular payments,
the present value, PV, and future value, FV, are set to 0.
CHECK Your Understanding
Draw a timeline representing an annuity of semi-annual payments of
1.
$450 for 3 years at 12%/a compounded semi-annually. Use the
timeline to show how the future value of each payment contributes
toward the future value of the annuity.
Geoff and Marilynn are each investing in a 3-year Registered
2.
Retirement Savings Plan (RRSP) fund at 6%/a compounded quarterly.
Geoff will make one deposit of $3600 at the beginning of the first
year. Marilynn will make a $300 deposit at the end of March and will
continue to contribute $300 every quarter until the end of the third
year. Determine the difference in the future values.
PRACTISING
Determine the amount of each annuity.
3.
Regular deposits of $500 every 6 months for 4 years at 8%/a
a)
compounded semi-annually
Regular deposits of $200 every month for 8 years at 10%/a
b)
compounded monthly
498
Chapter 8
NEL
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