Question

In: Finance

You are loaned $100,000 and pay this back by making constant payments at the end of each year for 40 years.

You are loaned $100,000 and pay this back by making constant payments at the end of each year for 40 years. If effective annual interest is i = 3% then find when the outstanding balance first falls below $50,000.

Solutions

Expert Solution

A loan repays itself by a fixed payment every year. We have to find when the outstanding balance falls below 50,000 for the first time.

 

When a loan is amortized under a fixed payment, a part of the payment goes towards reducing the balance of the loan. Hence, the balance outstanding keeps falling throughout the term of the loan.

 

First we will calculate the annual payment, P on the loan.

 

Let us assume that outstanding balance falls below B = 50,000 for the firs time when there are still m payments left to be done.

 

Then the balance loan = PV of the m remaining payment P as annuity

 

 

Hence, the loan balance will fall below 50,000 for the first time after 26 years.

Hence, the loan balance will fall below 50,000 for the first time after 26 years.

Junaid answered 1 year ago
Next > < Previous

Related Solutions

You will make deposits of $1,000 at the end of each year for 40 years in...
You will make deposits of $1,000 at the end of each year for 40 years in your investment account. After the 40th deposit, you will immediately withdraw all money from the account to buy a retirement annuity for 35 years with equal annual payments (paid at year-end) from a life insurance company. If the annual rate of return over the entire period (75 years) is 5%, how much is the annual payment from the insurance company? The amount of your...
An investment will pay $10 at the end of each of the next 3 years, $40...
An investment will pay $10 at the end of each of the next 3 years, $40 at the end of Year 4, $50 at the end of Year 5, and $60 at the end of Year 6. If other investments of equal risk earn 8% annually, what is this investment’s future value?
An investment will pay $16,100 at the end of each year for eight years and a...
An investment will pay $16,100 at the end of each year for eight years and a one-time payment of $161,000 at the end of the eighth year. (FV of $1, PV of $1, FVA of $1, and PVA of $1) (Use the appropriate factor(s) from the tables provided.) Determine the present value of this investment using a 6% annual interest rate. (Round your answer to the nearest whole dollar.)
You have borrowed $100,000 on a 40-year mortgage with monthly payments. The annual interest rate is...
You have borrowed $100,000 on a 40-year mortgage with monthly payments. The annual interest rate is 16 percent. How much will you pay over the course of the loan? With four years left on the loan, how much will you still owe? Excel
You have borrowed $100,000 on a 40-year mortgage with monthly payments. The annual interest rate is...
You have borrowed $100,000 on a 40-year mortgage with monthly payments. The annual interest rate is 16 percent. How much will you pay over the course of the loan? With four years left on the loan, how much will you still owe? excel
You take out a 25 year, $275, 000 mortgage with constant payments at the end of...
You take out a 25 year, $275, 000 mortgage with constant payments at the end of each month and i (12) = 6%. After 15 years, you wish to refinance the mortgage with a 10 year mortgage (also with constant payments at the end of each month) so that you pay $100 less each month than you originally were paying. Find the monthly nominal interest rate corresponding to this new mortgage
A mortgage of $100,000 is amortized over 25 years using level payments at the end of...
A mortgage of $100,000 is amortized over 25 years using level payments at the end of each quarter and the first interest payment at the end of the first quarter is $2411.37. Calculate the 62nd principal payment amount. a. 1074.21 b. 1048.92 c. 1100.11 d. 1024.22 e. None of these answers
An investment will pay you $100 at the end of each of the next 3 years,...
An investment will pay you $100 at the end of each of the next 3 years, $200 at the end of Year 4, $300 at the end of Year 5, and $500 at the end of Year 6. If the investment earns 8% annually, what is its future value?
Suppose you plan to borrow $300,000 from a financial institution and you are required to repay the loan by making equal annual payments for five years (payment at the end of each year).
  Suppose you plan to borrow $300,000 from a financial institution and you are required to repay the loan by making equal annual payments for five years (payment at the end of each year). The interest rate for the loan is 3.5% per year. Show your answers correct to two decimal points. Calculate the annual payment required. Prepare an amortization schedule for the loan for each year according to the following format. Year Beginning balance Annual payment Interest paid Principal...
You purchase a 10 year annuity with payments at the end of each year for $10,000
You purchase a 10 year annuity with payments at the end of each year for $10,000 (where for this annuity effective annual interest is 4%). Immediately after you receive payments, you deposit the payment into an account earning 5% effective annual interest. How much is in this account at the end of 10 years? Use this to find the equivalent effective annual interest rate for this $10, 000 investment over this 10 year period.
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT