Find The Present Value Of An Ordinary Annuity Which Has Payments Of $ 2100 \$2100 $2100 Per Year For 15 Years At 6 % 6\% 6% Compounded Annually.What Formula Is Used To Find The Present Value? Select The Correct Answer Below And Fill In The Answer

What is an Ordinary Annuity?

An ordinary annuity is a type of annuity where a fixed amount of money is paid at the end of each period, for a fixed number of periods. In this case, we have an ordinary annuity with payments of $\$2100$ per year for 15 years.

The Formula for Present Value of an Ordinary Annuity

The present value of an ordinary annuity can be calculated using the formula:

$$P = \frac{PMT \times (1 - (1 + r)^{-n})}{r}$$

Where:

• $P$ is the present value of the annuity
• $PMT$ is the annual payment
• $r$ is the interest rate per period
• $n$ is the number of periods

How to Use the Formula

To find the present value of the ordinary annuity, we need to plug in the values into the formula:

• $PMT = \$2100$
• $r = 6\% = 0.06$
• $n = 15$ years

Substituting these values into the formula, we get:

$$P = \frac{\$2100 \times (1 - (1 + 0.06)^{-15})}{0.06}$$

Calculating the Present Value

To calculate the present value, we need to evaluate the expression inside the brackets first:

$$(1 + 0.06)^{-15} = 0.419$$

Now, we can substitute this value back into the formula:

$$P = \frac{\$2100 \times (1 - 0.419)}{0.06}$$

$$P = \frac{\$2100 \times 0.581}{0.06}$$

$$P = \frac{\$1217.10}{0.06}$$

$$P = \$20,283.33$$

Conclusion

The present value of the ordinary annuity is $\$20,283.33$. This means that if we were to receive $\$2100$ per year for 15 years at an interest rate of $6\%$ compounded annually, the present value of the annuity would be $\$20,283.33$.

Example Use Case

This formula can be used to calculate the present value of any ordinary annuity, where a fixed amount of money is paid at the end of each period, for a fixed number of periods. For example, if we were to receive $\$5000$ per year for 10 years at an interest rate of $8\%$ compounded annually, the present value of the annuity would be:

$$P = \frac{\$5000 \times (1 - (1 + 0.08)^{-10})}{0.08}$$

$$P = \frac{\$5000 \times 0.623}{0.08}$$

$$P = \frac{\$3115}{0.08}$$

$$P = \$39,062.50$$

Conclusion

In conclusion, the present value of an ordinary annuity can be calculated using the formula:

$$P = \frac{PMT \times (1 - (1 + r)^{-n})}{r}$$

Where:

• $P$ is the present value of the annuity
• $PMT$ is the annual payment
• $r$ is the interest rate per period
• $n$ is the number of periods

Q: What is the difference between an ordinary annuity and an annuity due?

A: An ordinary annuity is a type of annuity where a fixed amount of money is paid at the end of each period, for a fixed number of periods. An annuity due, on the other hand, is a type of annuity where a fixed amount of money is paid at the beginning of each period, for a fixed number of periods.

Q: How do I calculate the present value of an annuity due?

A: To calculate the present value of an annuity due, you can use the formula:

$$P = \frac{PMT \times (1 - (1 + r)^{-n})}{r} \times (1 + r)$$

Where:

• $P$ is the present value of the annuity due
• $PMT$ is the annual payment
• $r$ is the interest rate per period
• $n$ is the number of periods

Q: What is the formula for calculating the present value of a growing annuity?

A: The formula for calculating the present value of a growing annuity is:

$$P = \frac{PMT \times (1 + g) \times (1 - (1 + r)^{-n})}{r}$$

Where:

• $P$ is the present value of the growing annuity
• $PMT$ is the annual payment
• $g$ is the growth rate per period
• $r$ is the interest rate per period
• $n$ is the number of periods

Q: How do I calculate the present value of a perpetuity?

A: To calculate the present value of a perpetuity, you can use the formula:

$$P = \frac{PMT}{r}$$

Where:

• $P$ is the present value of the perpetuity
• $PMT$ is the annual payment
• $r$ is the interest rate per period

Q: What is the difference between a present value and a future value?

A: The present value of an annuity is the value of the annuity today, while the future value of an annuity is the value of the annuity at a future date. The present value takes into account the time value of money, while the future value does not.

Q: How do I calculate the future value of an annuity?

A: To calculate the future value of an annuity, you can use the formula:

$$FV = PMT \times \frac{(1 + r)^n - 1}{r}$$

Where:

• $FV$ is the future value of the annuity
• $PMT$ is the annual payment
• $r$ is the interest rate per period
• $n$ is the number of periods

Q: What is the formula for calculating the present value of a bond?

A: The formula for calculating the present value of a bond is:

$$P = \frac{PMT \times (1 - (1 + r)^{-n})}{r} + \frac{FV}{(1 + r)^n}$$

Where:

• $P$ is the present value of the bond
• $PMT$ is the annual payment
• $r$ is the interest rate per period
• $n$ is the number of periods
• $FV$ is the face value of the bond

Conclusion

In conclusion, the present value of an ordinary annuity can be calculated using the formula:

$$P = \frac{PMT \times (1 - (1 + r)^{-n})}{r}$$

Where:

• $P$ is the present value of the annuity
• $PMT$ is the annual payment
• $r$ is the interest rate per period
• $n$ is the number of periods

This formula can be used to calculate the present value of any ordinary annuity, where a fixed amount of money is paid at the end of each period, for a fixed number of periods.