Value Worksheet With Answer Key Page 8
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8Marcel would like to take a vacation to Mexico during March break,
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6 months from today. The trip will cost $3600. Marcel deposits $195
into an account at the end of each month for the next 8 months at
9%/a compounded monthly. Will he have enough money to pay for
his trip? Explain.
Mario deposits $25 at the end of each month for 4 years into an
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account that pays 9.6%/a compounded monthly. He then makes no
further deposits and no withdrawals. Determine the balance 10 years
after his last deposit.
Darcey would like to accumulate $80 000 in savings before she retires
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A
20 years from now. She intends to make the same deposit at the end of
each month in an RRSP that pays 6.3%/a compounded monthly.
Draw a timeline to represent the annuity.
a)
What regular payment will let Darcey reach her goal?
b)
Suppose Darcey decides to wait 5 years before starting her
c)
deposits. What regular payment would she have to make to reach
the same goal?
Describe the payments, interest rates, and type of compounding
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necessary for a 15-year annuity with a future value between $10 000
and $12 000. Use two different compounding periods, each at a
different interest rate, to modify the amounts shown.
Which annuity will earn the greater amount at the end of 2 years?
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K
Justify your answer.
$50 at the end of every week at 5%/a compounded weekly
a)
$2600 at the end of every year at 5%/a compounded annually
b)
Explain why the formula for calculating the accumulated value of a
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C
simple annuity would not work if the interest-compounding period
did not coincide with the payment interval.
Extending
Byron has just bought a car for $25 000. He plans to replace it with a
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similar car in 3 years. At that time, his current car will be worth about
one-third of its current value, and he will trade it for the new car. He
will start saving for the rest of the cost by investing every month into
an account paying 4.5%/a compounded monthly. How much should
each payment be so that he can pay cash for the new car?
Nastassia borrowed $4831 at 7.5%/a compounded monthly. She has
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made 30 monthly payments of $130 each. She is now in a position to
pay off the balance. What is that balance?
500
Chapter 8
NEL
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