TUTORIAL WITH WORK SHOWN FOR THE FOLLOWING QUESTIONS

1. Find the periodic payment R required to amortize a loan of P dollars over t years with interest charged at the rate of r%/year compounded m times a year. (Round your answer to the nearest cent.)

2. Find the periodic payment R required to amortize a loan of P dollars over t years with interest charged at the rate of r%/year compounded m times a year. (Round your answer to the nearest cent.)

3. Find the periodic payment R required to accumulate a sum of S dollars over t years with interest earned at the rate of r%/year compounded m times a year. (Round your answer to the nearest cent.)

4. Find the periodic payment R required to accumulate a sum of S dollars over t years with interest earned at the rate of r%/year compounded m times a year. (Round your answer to the nearest cent.)

5. Suppose payments will be made for 9 years at the end of each month into an ordinary annuity earning interest at the rate of 6.25%/year compounded monthly. If the present value of the annuity is $34,000, what should be the size of each payment? (Round your answer to the nearest cent.)

6. What monthly payment is required to amortize a loan of $50,000 over 11 years if interest at the rate of 10%/year is charged on the unpaid balance and interest calculations are made at the end of each month? (Round your answer to the nearest cent.)

7. The Flemings secured a bank loan of $304,000 to help finance the purchase of a house. The bank charges interest at a rate of 8%/year on the unpaid balance, and interest computations are made at the end of each month. The Flemings have agreed to repay the loan in equal monthly installments over 25 years. What should be the size of each repayment if the loan is to be amortized at the end of the term? (Round your answer to the nearest cent.)

8. A group of private investors purchased a condominium complex for $3.5 million. They made an initial down payment of 15% and obtained financing for the balance. If the loan is to be amortized over 14 years at an interest rate of 15% per year compounded quarterly, find the required quarterly payment. (Round your answer to the nearest cent.)

9. Carl is the beneficiary of a $20,000 trust fund set up for him by his grandparents. Under the terms of the trust, he is to receive the money over an 8-year period in equal installments at the end of each year. If the fund earns interest at the rate of 8%/year compounded annually, what amount will he receive each year? (Round your answer to the nearest cent.)

10. Joe secured a loan of $15,000 two years ago from a bank for use toward his college expenses. The bank charges interest at the rate of 5%/year compounded monthly on his loan. Now that he has graduated from college, Joe wishes to repay the loan by amortizing it through monthly payments over 13 years at the same interest rate. Find the size of the monthly payments he will be required to make. (Round your answer to the nearest cent.)

11. Jennifer is the owner of a video game and entertainment software retail store. She is currently planning to retire in 30 years and wishes to withdraw $7,000/month for 20 years from her retirement account starting at that time. How much must she contribute each month for 30 years into a retirement account earning interest at the rate of 5%/year compounded monthly to meet her retirement goal? (Round your answer to the nearest cent.)

12. Since he was 20 years old, Ben has been depositing $275 at the end of each month into a tax-free retirement account earning interest at the rate of 6.5%/year compounded monthly. Larry, who is the same age as Ben, decided to open a tax-free retirement account 5 years after Ben opened his. If Larry's account earns interest at the same rate as Ben's, determine how much Larry should deposit each month into his account so that both men will have the same amount of money in their accounts at age 65. (Round your answer to the nearest cent.)

13. Five years ago, Diane secured a bank loan of $320,000 to help finance the purchase of a loft in the San Francisco Bay area. The term of the mortgage was 30 years, and the interest rate was 10%/year compounded monthly on the unpaid balance. Because the interest rate for a conventional 30-year home mortgage has now dropped to 7%/year compounded monthly, Diane is thinking of refinancing her property. (Round your answers to the nearest cent.)

(a) What is Diane's current monthly mortgage payment?

(b) What is Diane's current outstanding principal?

(c) If Diane decides to refinance her property by securing a 30-year home mortgage loan in the amount of the current outstanding principal at the prevailing interest rate of 7%/year compounded monthly, what will be her monthly mortgage payment?

(d) How much less will Diane's monthly mortgage payment be if she refinances?

1. The Martinezes are planning to refinance their home. The outstanding balance on their original loan is $125,000. Their finance company has offered them two options. (Assume there are no additional finance charges. Round your answers to the nearest cent.)

Option A: A fixed-rate mortgage at an interest rate of 6.5%/year compounded monthly, payable over a 30-year period in 360 equal monthly installments.

Option B: A fixed-rate mortgage at an interest rate of 6.25%/year compounded monthly, payable over a 15-year period in 180 equal monthly installments.

(a) Find the monthly payment required to amortize each of these loans over the life of the loan.

(b) How much interest would the Martinezes save if they chose the 15-year mortgage instead of the 30-year mortgage?