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Suppose that your bank pays interest, compounded quarterly.
Use Table to find how much should be deposited now to yield an
annuity payment of at the end of each three months, for 3 years
(Round your answer to the nearest cent.)

Ask by Summers Rose. in the United States
Mar 21,2025

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You should deposit approximately $14,156.09 now to receive $1,300 at the end of each three months for 3 years with a 6% annual interest rate compounded quarterly.

Solución

We are given an annuity with the following parameters:
  • Periodic payment:
  • Annual interest rate: compounded quarterly, so the periodic rate is
  • Number of years: 3, so the number of quarterly periods is
The present value of an ordinary annuity is calculated by the formula
Substitute the given values into the formula:
Now, calculate :
Thus,
Next, compute the factor in the formula:
Finally, multiply by :
Therefore, the amount that should be deposited now is approximately .

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The Deep Dive

To determine how much should be deposited now to yield an annuity payment of every three months for 3 years at an interest rate of compounded quarterly, you can use the present value of an annuity formula. Since the payments are made quarterly, divide the annual interest rate by 4 (to get per quarter) and the number of years by 4 (to get 12 total payments).
Using the present value of annuity formula:
Where:
Substituting the values:
Calculating this provides the present value required for the annuity. Round the answer to the nearest cent. The resulting present value is approximately .
So, you’d need to deposit approximately now to generate every three months over the next 3 years. 📈💰

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