Ian loaned his friend $20,000 to start a new business. He considers this loan to be an investment, and therefore requires his friend to pay him an interest rate of 7% on the loan. He also expects his friend to pay back the loan over the next four years by making annual payments at the end of each year. Ian texted and asked that you help him calculate the annual payments that he should expect to receive so that he can recover his initial investment and earn the agreed-upon 7% on his investment. Calculate the annual payment and complete the following capital recovery schedule: Year Beginning Amount Payment Interest Paid Principal Paid Ending Balance 1 $20,000.00 2 3 4 $0.01
Ian loaned his friend $20,000 to start a new business. He considers this loan to be an investment, and therefore requires his friend to pay him an interest rate of 7% on the loan. He also expects his friend to pay back the loan over the next four years by making annual payments at the end of each year. Ian texted and asked that you help him calculate the annual payments that he should expect to receive so that he can recover his initial investment and earn the agreed-upon 7% on his investment. Calculate the annual payment and complete the following capital recovery schedule: Year Beginning Amount Payment Interest Paid Principal Paid Ending Balance 1 $20,000.00 2 3 4 $0.01
Chapter4: Time Value Of Money
Section: Chapter Questions
Problem 23PROB
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10. Loan amortization and capital recovery
Ian loaned his friend $20,000 to start a new business. He considers this loan to be an investment, and therefore requires his friend to pay him an interest rate of 7% on the loan. He also expects his friend to pay back the loan over the next four years by making annual payments at the end of each year. Ian texted and asked that you help him calculate the annual payments that he should expect to receive so that he can recover his initial investment and earn the agreed-upon 7% on his investment.
Calculate the annual payment and complete the following capital recovery schedule:
Year
|
Beginning Amount
|
Payment
|
Interest Paid
|
Principal Paid
|
Ending Balance
|
---|---|---|---|---|---|
1 | $20,000.00 | ||||
2 | |||||
3 | |||||
4 | $0.01 |
Expert Solution
Step 1
Annuity: The amount accumulated by periodic deposits is known as an annuity.
The loan is a value that is borrowed from external sources like banks and this amount is repaid later in fixed installments which includes part of principal and interest. This is known as loan amortization.
To calculate the annual payment and to complete the capital recovery schedule, we have to use the following formula,
Where P is the principal amount
i = the interest rate
N = the number of years
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