A local bank advertises the following deal: Pay us $100 at the end of each year for 11 years and then we will pay you (or your beneficiaries) $100 at the end of each year forever.
a. Calculate the present value of your payments to the bank if the interest rate is 9.00%.
Answer
b. What is the present value of a $100 perpetuity deferred for 11 years if the interest rate is 9.00%.
Answer
c. Is this a good deal?
Answer
No
Explanation
Some values below may show as rounded for display purposes, though unrounded numbers should be used for actual calculations.
a.
| PV | = | C((1 / r) – {1 / [r(1 + r)t]}) |
| = | $100 × ((1 / 0.0900) – {1 / [0.0900(1.0900)11]}) | |
| = | $680.52 |
b.
| PV10 | = | C / r |
| = | $100 / .0900 | |
| = | $1,111.11 |
This is the present value of the annuity in 10 years. You now need to find the present value as of today.
| PV | = | FV / (1 + r)t |
| = | $1,111.11 / 1.090011 | |
| = | $430.59 |
c.
This is not a good deal if you can earn 9.00% because today’s value of the bank’s payments to you less than the value of your payments to the bank.
Calculator computations:
a.
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Enter
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11
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9.00
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-100
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N
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I/Y
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PV
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PMT
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FV
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Solve for
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680.52
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b.
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Enter
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11
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9.00
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-1,111.11 | ||||||||||||
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N
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I/Y
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PV
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PMT
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FV
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Solve for
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430.59
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