FINANCIAL ACCOUNTING
FINANCIAL ACCOUNTING
10th Edition
ISBN: 9781259964947
Author: Libby
Publisher: MCG
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**Problem on Present Value of Annuity**

**Question:**

Whispering Winds Corp. has just purchased equipment that requires annual payments of $75,000 to be paid at the end of each of the next 5 years. The appropriate discount rate is 15%. What is the present value of the payments?

**Options:**

- $251,412
- $184,188
- $287,348
- $297,213

---

To solve this problem, we need to calculate the present value of an annuity. The formula for the present value of an annuity is:

\[ PV = P \times \left( \frac{1 - (1 + r)^{-n}}{r} \right) \]

where:
- \( PV \) is the present value
- \( P \) is the annual payment (in this case, $75,000)
- \( r \) is the discount rate (in this case, 15% or 0.15)
- \( n \) is the number of years (in this case, 5)

Let's apply the formula:

\[ PV = 75{,}000 \times \left( \frac{1 - (1 + 0.15)^{-5}}{0.15} \right) \]

First, calculate \((1 + r)^{-n}\):

\[ (1 + 0.15)^{-5} = (1.15)^{-5} \approx 0.4972 \]

Then, calculate the rest of the equation:

\[ 75{,}000 \times \left( \frac{1 - 0.4972}{0.15} \right) = 75{,}000 \times \left( \frac{0.5028}{0.15} \right) \approx 75{,}000 \times 3.352 \approx 251{,}400 \]

Hence, the closest option is:

- $251,412

Therefore, the correct answer is $251,412.
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Transcribed Image Text:**Problem on Present Value of Annuity** **Question:** Whispering Winds Corp. has just purchased equipment that requires annual payments of $75,000 to be paid at the end of each of the next 5 years. The appropriate discount rate is 15%. What is the present value of the payments? **Options:** - $251,412 - $184,188 - $287,348 - $297,213 --- To solve this problem, we need to calculate the present value of an annuity. The formula for the present value of an annuity is: \[ PV = P \times \left( \frac{1 - (1 + r)^{-n}}{r} \right) \] where: - \( PV \) is the present value - \( P \) is the annual payment (in this case, $75,000) - \( r \) is the discount rate (in this case, 15% or 0.15) - \( n \) is the number of years (in this case, 5) Let's apply the formula: \[ PV = 75{,}000 \times \left( \frac{1 - (1 + 0.15)^{-5}}{0.15} \right) \] First, calculate \((1 + r)^{-n}\): \[ (1 + 0.15)^{-5} = (1.15)^{-5} \approx 0.4972 \] Then, calculate the rest of the equation: \[ 75{,}000 \times \left( \frac{1 - 0.4972}{0.15} \right) = 75{,}000 \times \left( \frac{0.5028}{0.15} \right) \approx 75{,}000 \times 3.352 \approx 251{,}400 \] Hence, the closest option is: - $251,412 Therefore, the correct answer is $251,412.
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