143k views
3 votes
Please calculate the present value of each amount in the scenarios, rounded to the nearest dollar. Note that the interest rates are compounded annually. Jacob takes out a student loan at an interest rate of 6.0% . Jacob plans to make no payments before paying $10,358 to his lender after three years to pay off the loan. $ Tommy buys a government-issued bond. The bond has a rate of 3.0% , and he will receive $4,762 when he cashes it in in five years. $ Steve takes out a small business loan to open a deli. The loan has a rate of 7.0% . Steve will repay the loan with a single payment of $14,681 made in six years.

User Polymath
by
8.2k points

2 Answers

6 votes

Final answer:

To calculate the present value of each amount, use the present value formula. Jacob's loan has a present value of $9,227, Tommy's bond has a present value of $4,285, and Steve's loan has a present value of $10,459.

Step-by-step explanation:

To calculate the present value of each amount, we need to use the present value formula. The formula is:

Present Value = Future Value / (1 + Interest Rate)^Number of Periods

For Jacob's student loan, the future value is $10,358, the interest rate is 6%, and the number of periods is 3 years. Plugging these values into the formula, we get:

Present Value = $10,358 / (1 + 0.06)^3

Calculating this gives us a present value of $9,227.

For Tommy's government bond, the future value is $4,762, the interest rate is 3%, and the number of periods is 5 years. Plugging these values into the formula, we get:

Present Value = $4,762 / (1 + 0.03)^5

Calculating this gives us a present value of $4,285.

For Steve's small business loan, the future value is $14,681, the interest rate is 7%, and the number of periods is 6 years. Plugging these values into the formula, we get:

Present Value = $14,681 / (1 + 0.07)^6

Calculating this gives us a present value of $10,459.

User Klozovin
by
8.6k points
1 vote

Final answer:

The present value of Jacob's loan payment is $8,700, Tommy's bond is $4,104, and Steve's loan repayment is $9,780, all rounded to the nearest dollar.

Step-by-step explanation:

To calculate the present value of payments to be made in the future, we can use the formula PV = FV / (1 + r)^n, where PV is the present value, FV is the future value of the payment, r is the annual interest rate (as a decimal), and n is the number of years until the payment will be made.

For Jacob's student loan with a future payment of $10,358 at a 6% interest rate after three years, the present value calculation is as follows:

PV = $10,358 / (1 + 0.06)^3

PV = $10,358 / (1.191016)

PV = $8,700 (rounded to the nearest dollar)

Tommy's government-issued bond, with a future payment of $4,762 at a 3% interest rate after five years, would have a present value of:

PV = $4,762 / (1 + 0.03)^5

PV = $4,762 / (1.159274)

PV = $4,104 (rounded to the nearest dollar)

Lastly, Steve's small business loan, with a future payment of $14,681 at a 7% interest rate in six years, has a present value given by:

PV = $14,681 / (1 + 0.07)^6

PV = $14,681 / (1.501002)

PV = $9,780 (rounded to the nearest dollar)

User JP Illanes
by
8.6k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.