In two years, a bond will start paying out an annual annuity of 20:-, after which the annuity will increase by 2% per year. The bond will pay out an annuity for 30 years. No face value has been paid in the last year. What does the bond cost today? Use a return requirement of 7%. Ignore
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question 1
In two years, a bond will start paying out an annual
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- Use the tables in Appendix B to answer the following questions. A. If you would like to accumulate $4,200 over the next 6 years when the interest rate is 8%, how much do you need to deposit in the account? B. If you place $8,700 in a savings account, how much will you have at the end of 12 years with an interest rate of 8%? C. You invest $2,000 per year, at the end of the year, for 20 years at 10% interest. How much will you have at the end of 20 years? D. You win the lottery and can either receive $500,000 as a lump sum or $60,000 per year for 20 years. Assuming you can earn 3% interest, which do you recommend and why?You put $600 in the bank for 3 years at 15%. A. If Interest Is added at the end of the year, how much will you have in the bank after one year? Calculate the amount you will have in the bank at the end of year two and continue to calculate all the way to the end of the third year. B. Use the future value of $1 table In Appendix B and verify that your answer is correct.Question 1. Assume you have just taken a 30-year mortgage of $550,000 at 9% with monthly compounding. Further, suppose that in 10 years (immediately after the 120th payment) interest rates fall to 6% with monthly compounding. You decide to refinance at that time to a 15-year loan at the new lower rate. Assume refinancing costs are 2% of the amount refinanced and will be rolled into the new loan. Find your new payment for the refinanced loan. Question 2. Suppose you deposit $100,000 per year in a savings account paying 8% interest for 10 years. You wish to withdraw the funds in 5 equal installments, one year apart, starting in year 11 and have a balance remaining in your account of $75,000 immediately after you make your fifth withdrawal. How much can you withdraw per year? HINT: A timeline will help with this.
- 10. You borrow $100,000 from a bank for 30 years at an APR of 10.5%. What is the monthly payment? If you must pay two points up front, meaning that you only get $98,000 from the bank, what is the true APR on the mortgage loan? 11. Suppose that the mortgage loan described in question 10 is a one-year adjustable rate mortgage (ARM), which means that the 10.5% interest applies for only the first year. If the interest rate goes up to 12% in the second year of the loan, what will your new monthly payment be?4. If you borrow $200,000 at an APR of 8% for 25 years, you will pay more per month than borrow the money for 30 years at 8%. a. What is the monthly payment on the 25-year mortgage, to the nearest cent? b. What is the total interest paid on the 25-year mortgage? c. What is the monthly payment on the 30-year mortgage? d. What is the total interest paid on the 30-year mortgage? e. How much more interest is paid on the 30-year loan? Round to the nearest dollar. f. What is the difference between the monthly payments of the two different loans? Round to the nearest dollar.Amortization, Loan & InflationSuppose you take out a $100,000, 20- year mortgage loan to purchase a condo. The interest rate is 6%. Assume you make payments on the loan annually at the end of each year.a. What fraction of the initial loan payment is interest?b. What fraction of the initial loan is amortized? c. If the inflation rate is 2%, what are the real values of the first& last (year-end) payments?
- 2B. a. Suppose we have a four year fixed-payment loan with $900 payments made at the end of each year. Given a market interest rate of 7 percent, how much was initially borrowed?Amortizing loans Suppose that you take out a 30-year mortgage loan of $200,000 at an interest rate of 10%. a. What is your total monthly payment? b. How much of the first month's payment goes to reduce the size of the loan? c. How much of the payment after two years goes to reduce the size of the loan?Problem 1: Finance in Perpetuity You are offered one of the following two options for free. Option A includes a fixed cash flow of 250$ every year forever that starts right now (first payment at the end of this year (t = 1)). Option B includes a fixed cash flow of 250$ every year forever, but it starts a year later (first payment at the end of the next year (t = 2)). Interest rates are at 8% per year for every maturity. 1. What is the present value of Option A when it starts (at t = : 0)? 2. What is the present value of Option B when it starts (at t = 1)? 3. Which one should you pick and why?
- 4. You are offered an annuity that will pay R17,000 per year for 7 years (the first payment will be made today). If you feel that the appropriate discount rate is 11%, what is the annuity worth to you today? 15. If you deposit R15,000 per year for 9 years (each deposit is made at the beginning of each year) in an account that pays an annual interest rate of 8%, what will your account be worth at the end of 9 years?Suppose that the mortgage loan described in question 10 is a one-year adjustable rate mortgage (ARM), which means that the 10.5% interest applies for only the first year.If the interest rate goes up to 12% in the second year of the loan, what will your new monthly payment be?1. What is the future value of an ordinary annuity that promises $60,000 per year for 10 years if the appropriate interest rate is 4%? 2. What is the future value of an annuity due that promises $60,000 per year for 10 years if the appropriate interest rate is 4%? 3. You recently received a credit card that quotes an annual percentage rate (APR) of 24%. The card requires monthly payments. What is the effective annual rate (EAR)?