QuestionCalculate the present value of Ben's \$100,000 sale: \$20,000 today + \$20,000 for 4 years at 4% interest. Choices: A. \$87,096 B. \$88,384 C. \$92,598 D. \$93,964

Studdy Solution

STEP 1

Assumptions1. The total selling price of the business is $100,000. The purchaser will pay$ 20,000 today and $20,000 every year for the next four years3. The interest rate for the lump-sum investment is4% annually4. We are to find the present value of all five payments

STEP 2

The present value (PV) of a future payment can be calculated using the formula $PV = \frac{V}{(1 + r)^n}$ where- $V$ is the future value of the payment- $r$ is the interest rate- $n$ is the number of periods until the payment is received

STEP 3

First, let's calculate the present value of the payment received today. Since it's received today, its present value is the same as its face value.
$PV_{today} = \$20,000$

STEP 4

Now, let's calculate the present value of the payment received in one year.
$PV_{1\, year} = \frac{\$20,000}{(1 +0.04)^1}$

STEP 5

Calculate the present value of the payment received in two years.
$PV_{2\, years} = \frac{\$20,000}{(1 +0.04)^2}$

STEP 6

Calculate the present value of the payment received in three years.
$PV_{3\, years} = \frac{\$20,000}{(1 +0.04)^3}$

STEP 7

Calculate the present value of the payment received in four years.
$PV_{4\, years} = \frac{\$20,000}{(1 +0.04)^4}$

STEP 8

Now, let's add up all the present values to get the total present value of all five payments.
$Total\, PV = PV_{today} + PV_{1\, year} + PV_{2\, years} + PV_{3\, years} + PV_{4\, years}$

STEP 9

Plug in the values for each present value to calculate the total present value.
Total\, PV = \$20,000 + \frac{\$20,000}{( +.04)^} + \frac{\$20,000}{( +.04)^2} + \frac{\$20,000}{( +.04)^3} + \frac{\$20,000}{( +.04)^4}

STEP 10

Calculate the total present value.
The total present value of all five payments is approximately $\$92,598$ .
Therefore, the correct answer is C. $\$92,598$ .

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QuestionCalculate the present value of Ben's \$100,000 sale: \$20,000 today + \$20,000 for 4 years at 4% interest. Choices: A. \$87,096 B. \$88,384 C. \$92,598 D. \$93,964

Studdy Solution

STEP 1

Assumptions1. The total selling price of the business is $100,000. The purchaser will pay$ 20,000 today and $20,000 every year for the next four years3. The interest rate for the lump-sum investment is4% annually4. We are to find the present value of all five payments

STEP 2

The present value (PV) of a future payment can be calculated using the formula $PV = \frac{V}{(1 + r)^n}$ where- $V$ is the future value of the payment- $r$ is the interest rate- $n$ is the number of periods until the payment is received

STEP 3

First, let's calculate the present value of the payment received today. Since it's received today, its present value is the same as its face value.
$PV_{today} = \$20,000$

STEP 4

Now, let's calculate the present value of the payment received in one year.
$PV_{1\, year} = \frac{\$20,000}{(1 +0.04)^1}$

STEP 5

Calculate the present value of the payment received in two years.
$PV_{2\, years} = \frac{\$20,000}{(1 +0.04)^2}$

STEP 6

Calculate the present value of the payment received in three years.
$PV_{3\, years} = \frac{\$20,000}{(1 +0.04)^3}$

STEP 7

Calculate the present value of the payment received in four years.
$PV_{4\, years} = \frac{\$20,000}{(1 +0.04)^4}$

STEP 8

Now, let's add up all the present values to get the total present value of all five payments.
$Total\, PV = PV_{today} + PV_{1\, year} + PV_{2\, years} + PV_{3\, years} + PV_{4\, years}$

STEP 9

Plug in the values for each present value to calculate the total present value.
Total\, PV = \$20,000 + \frac{\$20,000}{( +.04)^} + \frac{\$20,000}{( +.04)^2} + \frac{\$20,000}{( +.04)^3} + \frac{\$20,000}{( +.04)^4}

STEP 10

Calculate the total present value.
The total present value of all five payments is approximately $\$92,598$ .
Therefore, the correct answer is C. $\$92,598$ .

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QuestionCalculate the present value of Ben's \$100,000 sale: \$20,000 today + \$20,000 for 4 years at 4% interest. Choices: A. \$87,096 B. \$88,384 C. \$92,598 D. \$93,964

Studdy Solution

STEP 1

STEP 2

The present value (PV) of a future payment can be calculated using the formulaPV=V(1+r)nPV = \frac{V}{(1 + r)^n}PV=(1+r)nV​where- VVV is the future value of the payment- rrr is the interest rate- nnn is the number of periods until the payment is received

STEP 3

First, let's calculate the present value of the payment received today. Since it's received today, its present value is the same as its face value.PVtoday=$20,000PV_{today} = \$20,000PVtoday​=$20,000

STEP 4

Now, let's calculate the present value of the payment received in one year.PV1 year=$20,000(1+0.04)1PV_{1\, year} = \frac{\$20,000}{(1 +0.04)^1}PV1year​=(1+0.04)1$20,000​

STEP 5

Calculate the present value of the payment received in two years.PV2 years=$20,000(1+0.04)2PV_{2\, years} = \frac{\$20,000}{(1 +0.04)^2}PV2years​=(1+0.04)2$20,000​

STEP 6

Calculate the present value of the payment received in three years.PV3 years=$20,000(1+0.04)3PV_{3\, years} = \frac{\$20,000}{(1 +0.04)^3}PV3years​=(1+0.04)3$20,000​

STEP 7

Calculate the present value of the payment received in four years.PV4 years=$20,000(1+0.04)4PV_{4\, years} = \frac{\$20,000}{(1 +0.04)^4}PV4years​=(1+0.04)4$20,000​

STEP 8

STEP 9

Plug in the values for each present value to calculate the total present value.Total\, PV = \$20,000 + \frac{\$20,000}{( +.04)^} + \frac{\$20,000}{( +.04)^2} + \frac{\$20,000}{( +.04)^3} + \frac{\$20,000}{( +.04)^4}

STEP 10

Calculate the total present value.The total present value of all five payments is approximately $92,598\$92,598$92,598.Therefore, the correct answer is C. $92,598\$92,598$92,598.

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The present value (PV) of a future payment can be calculated using the formula $PV = \frac{V}{(1 + r)^n}$ where- $V$ is the future value of the payment- $r$ is the interest rate- $n$ is the number of periods until the payment is received

First, let's calculate the present value of the payment received today. Since it's received today, its present value is the same as its face value.
$PV_{today} = \$20,000$

Now, let's calculate the present value of the payment received in one year.
$PV_{1\, year} = \frac{\$20,000}{(1 +0.04)^1}$

Calculate the present value of the payment received in two years.
$PV_{2\, years} = \frac{\$20,000}{(1 +0.04)^2}$

Calculate the present value of the payment received in three years.
$PV_{3\, years} = \frac{\$20,000}{(1 +0.04)^3}$

Calculate the present value of the payment received in four years.
$PV_{4\, years} = \frac{\$20,000}{(1 +0.04)^4}$

Plug in the values for each present value to calculate the total present value.
Total\, PV = \$20,000 + \frac{\$20,000}{( +.04)^} + \frac{\$20,000}{( +.04)^2} + \frac{\$20,000}{( +.04)^3} + \frac{\$20,000}{( +.04)^4}

Calculate the total present value.
The total present value of all five payments is approximately $\$92,598$ .
Therefore, the correct answer is C. $\$92,598$ .