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P6. Determine the present value if $5,000 is received in the future (i.e., at the end of each indicated time period) in each of the following situations : 

a. 5 percent for ten years

b. 7 percent for seven years 

c. 9 percent for four years

P9. Assume you are planning to invest $5,000 each year for six years and will earn 10 percent per year, determine the future value of this annuity if your first $5,000 is invested at the end of the first year.

P10. Determine the present value now of an investment of $3,000 made one year from now and a additional $3,000 made two years from now if the annual discount rate is 4 percent.

P 11. What is the present value of a loan that calls for the payment of $500 per year for six years if the discount rate is 10 percent and the first payment will be made one year from now? How would your answer change if the $500 per year occurred for ten years?

P12. Determine the annual payment on a $500,000, 12 percent business loan from a commercial bank that is to be amortized over a five year period.

P13. Determine the annual percent on a $15,000 loan that is to be amortized over a four year period and carries a 10 percent interest rate. Also prepared a loan amortization scheduled for this loan.

P15. Assume the bank loan requires an interest payment of $85 per year and a principal payment of $1000 at the end of the loan’s eight year life. 

a. At what amount could this loan be sold for to another bank if loans similar quality carried an 8.5 percent interest rate? That is , what would be the present value of the loan?

b. Now, if interest rates on other similar-quality loans are 10 percent , what would be the present value of this loan?

c. What would be the present value of the loan if the interest rate is 8 percent on similar-quality loans?