# Finance: Net Present Value and Rate

**Topics:**Net present value, Compound interest, Time value of money

**Pages:**7 (2892 words)

**Published:**September 2, 2013

Exercise

1. If you invest $1000 today at an interest rate of 10% per year, how much will you have 20 years from now, assuming no withdrawals in interim? 2. a. If you invest $100 every year from the next 20 years starting one year from today and you earn interest of 10% per year, how much will you have at the end of the 20 years? b. How much must you invest each year if you want to have $50000 at the end of the 20 years? 3. What is the present value of the following cash flows at an interest rate of 10% per year? (Hints: don’t need to use the financial keys of your calculator, just dome common sense) a. $100 received five years from now

b. $100 received 60 years from now

c. $100 received each year beginning one year from now and ending 10 years from now d. $100 each year beginning one year from now and continuing forever 4. You want to establish a “wasting” fund, which will provide your with $1000 per year for four years, at which time the fund will be exhausted. How much must you put in the fund now if you can earn 10% interest per year? 5. You take a one-year installment loan of $1000 at an interest rate of 12% per year (1% per month) to be repaid in 12 equal monthly payments. a. What is the monthly payment?

b. What is the total amount of interest paid over the 12-month term of the loan? 6. You are taking out a $100000 mortgage loan to be repaid over 25 years in 300 monthly payments. a. If the interest rate is 16% per year, what is the amount of the monthly payment? b. If you can only afford to pay $1000 per month, how large a loan could you take? c. If you can afford to pay $1500 per month and need to borrow $100000, how many months would it take to pay off the mortgage? d. If you can pay $1500 per month, need to borrow $100000, and want a 25-year mortgage, what is the highest interest rate you can pay? 7. In 1626 Peter Minuit purchased Manhattan Island from the Native Americans from about $24 worth of trinkets. If the tribe had taken cash instead and invested it to earn 6% per year compound annually, how much would the Indians have had in 360 years later? 8. You win a $1 million lottery, which pays you $50000 per year for 20 years. How much is your prize really worth, assuming an interest rate of 8% a year? 9. Your great aunt left you $20000 when she died. You can invest the money to earn 12% per year. If you spend $3540 per year out of this inheritance, how long will the money last? 10. You borrow $100000 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 $98000 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, which means that the 10.5% interest applies fro only the first year. If the interest rate goes up to 12% in the second year of the load, what will your new monthly payment be? 12. You just received a gift of $500 from your grandmother and you are thinking about saving this money for graduation, which his four years away. You have your choice between Bank A, which his paying 7% for one-year deposits, and Bank B, which his paying 6% on one-year deposits. Each bank compounds interest annually. a. What is the future value of your savings one year from today if you save your money in Bank A? Bank B? Which is the better decision? b. What saving s decision will most individual make? What likely reaction will Bank B have? 13. Sue Consultant has just been given a bonus of $2500 by her employer. She is thinking about using the money to start saving for the future. She can invest to earn an annual rate of interest of 10%. a. According to the Rule of 72, approximately how long will it take for Sue to increase her wealth to $5000? b. Exactly how long does it take?

14. Larry’s bank account has a “floating” interest rate on...

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