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Problem concerning time value of money

Problem 1) Joe will receive $175,000 in 50 years. His friends are jealous of him. What is his pot of gold worth today if the alternative investment rate is 14%

Problem 2) Sue will receive $12,000 a year for the next 15 years as a result of her patent. Using a 9% rate , should she be willing to sell her future rights now for $100,000.

Problem 3) Mike has been depositing $2,500 in a savings account each December starting in 1991. The account earns 5% compounded annually. How much will he have in December 2000. (Assume a deposit is made in December 2000).

Problem 4) If you owe $40,000 - payable at the end of seven years. How much should your creditor be willing to accept immediately if they could earn 12%.

Problem 5) Your rich uncle has offered you a choice of one of the three following alternatives

a) $10,000 now

b) $2,000 a year for 8 years - equal investments have earned 11%

c) $24,000 at the end of 8 years - equal investments have earned 11%

Problem 6) John started a paper route 1/1/95. Every 3 months , he deposited $500 in his bank account. The account earns 4% annually but is compounded quarterly. On 12/31/98 , he used the entire balance in his account to invest in a contract that pays 9% annually. How much will he have on 12/31/01?

Problem 7) Pete has just invested $6,250 for his son (age 1). The money will be used for his son's education in 17 years. He calculates that he will need $50,000 for the first year of college. What rate of return does he need?

Problem 8) Jane has just retired after 25 years. Her total pension has an accumulated value of $180,000. Her life expectancy is 15 more years. Her pension manager believes she can earn 9% on her assets. What will be her yearly income for the next 15 years?

Problem 9) You wish to retire in 18 years , at which time , you want to have accumulated enough money to receive an annuity of $14,000 a year for 20 years of retirement. During the period before retirement , you can 11% annually. after retirement you can earn 8% annually. What annual contributions will allow you to receive $14,000 annually.

Problem 10) If you borrow $15,618 and are required to pay the loan back in 7 equal annual instalments of $3,000. What is the interest rate associated with this loan?

Problem 11) If you borrow $17,000 and are required to pay it back in 20 equal annual instalments of $2,000 ; what is the approximate interest rate associated with the loan.

Problem 12) Joe Invests $50,000 in a project that is expected to yield a return of 8%, compounded semi-annually over the next 5 years. He will then take the proceeds & provide himself with a 10 year annuity. Assuming a 10% annual interest rate, how much will the annuity be?

Problem 13) Joe will receive $19,500 a year for the next 20 years as a payment for a song he has written. If a 10% rate is applied, should he be willing to sell out all future rights now for $160,000?

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## Q : Compounded annually with annual payments

What series of equal (uniform) payments is necessary to repay the following present amounts? a. $500 in 5 years at 10% compounded annually with annual payments