Question

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.

Answer 1

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.

Answer 2

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)