Problem 4. (2 points)
If you want to be paid from a 10 year ordinary annuity with a guar-
anteed rate of compounded annually, how much should
you pay for one of these annuities if you want to receive annual
payments of over the 10 year period?
(Note: Your answer should have a dollar sign and be accurate to
two decimal places)
Answer(s) submitted:

Ask by Hardy Stewart. in South Africa

Mar 23,2025

Question

Problem 4. (2 points)
If you want to be paid from a 10 year ordinary annuity with a guar-
anteed rate of compounded annually, how much should
you pay for one of these annuities if you want to receive annual
payments of over the 10 year period?
(Note: Your answer should have a dollar sign and be accurate to
two decimal places)
Answer(s) submitted:

Ask by Hardy Stewart. in South Africa

Mar 23,2025

UpStudy AI · Accepted Answer

We start with the present‐value formula for an ordinary annuity

$$
\text{PV} = R \cdot \frac{1 - (1 + r)^{-n}}{r},
$$

where  
$$ R = 10\,000 $$ is the annual payment,  
$$ r = 0.02967 $$ is the annual interest rate (expressed as a decimal), and  
$$ n = 10 $$ is the number of years.

Substitute the values into the formula:

$$
\text{PV} = 10\,000 \cdot \frac{1 - (1.02967)^{-10}}{0.02967}.
$$

Step 1. Compute $$(1.02967)^{10}$$.  
Multiplying year‐by‐year (or using logarithms) we find

$$
(1.02967)^{10} \approx 1.34658.
$$

Step 2. Compute the term $$(1.02967)^{-10}$$:

$$
(1.02967)^{-10} = \frac{1}{(1.02967)^{10}} \approx \frac{1}{1.34658} \approx 0.74287.
$$

Step 3. Compute the numerator:

$$
1 - (1.02967)^{-10} \approx 1 - 0.74287 = 0.25713.
$$

Step 4. Divide by the interest rate:

$$
\frac{0.25713}{0.02967} \approx 8.667.
$$

Step 5. Multiply by $$ 10\,000 $$ to obtain the present value:

$$
\text{PV} \approx 10\,000 \times 8.667 \approx 86\,670.
$$

Thus, you should pay approximately

$$
\$86\,670.00.
$$
You should pay approximately \$86,670.00 for the annuity.

Upstudy AI Solution

Answer

Solution

Bonus Knowledge

Related Questions

Latest Economics Questions