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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

Question

File Edit Format View Help
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

UpStudy AI · Accepted Answer

We are given an annuity with the following parameters:

- Periodic payment: $$ R = \$1{,}300 $$
- Annual interest rate: $$ 6\% $$ compounded quarterly, so the periodic rate is  
  $$
  i = \frac{6\%}{4} = 0.015
  $$
- Number of years: 3, so the number of quarterly periods is  
  $$
  n = 3 \times 4 = 12
  $$

The present value $$ PV $$ of an ordinary annuity is calculated by the formula

$$
PV = R \cdot \frac{1 - \left(1+i\right)^{-n}}{i}.
$$

Substitute the given values into the formula:

$$
PV = 1300 \cdot \frac{1 - (1.015)^{-12}}{0.015}.
$$

Now, calculate $$ (1.015)^{12} $$:

$$
(1.015)^{12} \approx 1.195565.
$$

Thus,

$$
(1.015)^{-12} \approx \frac{1}{1.195565} \approx 0.83666.
$$

Next, compute the factor in the formula:

$$
\frac{1 - 0.83666}{0.015} \approx \frac{0.16334}{0.015} \approx 10.8893.
$$

Finally, multiply by $$ R $$:

$$
PV \approx 1300 \times 10.8893 \approx 14{,}156.09.
$$

Therefore, the amount that should be deposited now is approximately $$\$14{,}156.09$$.
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.

File Edit Format View Help
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.)

Upstudy AI Solution

Answer

Solution

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File Edit Format View Help 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.)

Upstudy AI Solution

Answer

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File Edit Format View Help
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.)