financial mangment
Exercise 1.
(Future value) You invest a single amount of $12,000 for 5 years at 10 percent. At the end of 5 years you take the proceeds and invest them for 12 years at 15 percent. How much will you have after 17 years?
Answer: FV(5) = 12000*(1.1^5)=19326.12
FV(12) = 19326.12*(1.15^12)=103399.60
Exercise 2.
(Present value) The Western Sweepstakes has just informed you that you have won $1 million. The amount is to be paid out at the rate of $50,000 a year for the next 20 years. With a discount rate of 12 percent, what is the present value of your winnings?
Answer: (It is an annuity of 50’000 each year for 20 years)
Exercise 3
Rusty Steele will receive an annuity of $10,000 for the next 10 years; at the end of the next three years (that is year 11, 12, 13) he will get the following payments: $4,000, $7,000, and $9,000. At a discount rate of 10 percent, what is the present value of all future benefits?
Answer: In this case we have an annuity of 10000 for 10 years and then 3 single cash flows of 4000, 7000, and 9000 for years 11, 12 and 13. First we find the present value of the annuity:
Then we find the present value of the other three cash flows:
Then we sum PV with PV(11), PV(12) and PV(13).
Exercise 4
(Amortized loan) Your aunt borrows $50,000 from the bank at 10% interest for 8 years. What equal annual payments must be made to discharge the loan, plus pay the bank its required rate of interest (round to the nearest dollar)? How much of his first payment will be applied to interest? To principal? How much of her second payment will be applied to each?
Answer: The amount borrowed is the present value of an annuity. We need to find the payments of this annuity which correspond to the installments of the loan.
So,
= 9372
Beginning loan balance
PMT
Interest
Principal reduction (PMT – interest)
Loan ending balance = Beg. Balance – loan reduction
50000
9372
5000 (50000*0.1)
9372-5000=4372
50000-4372=45628
45628
9372
4562.8
(Future value) You invest a single amount of $12,000 for 5 years at 10 percent. At the end of 5 years you take the proceeds and invest them for 12 years at 15 percent. How much will you have after 17 years?
Answer: FV(5) = 12000*(1.1^5)=19326.12
FV(12) = 19326.12*(1.15^12)=103399.60
Exercise 2.
(Present value) The Western Sweepstakes has just informed you that you have won $1 million. The amount is to be paid out at the rate of $50,000 a year for the next 20 years. With a discount rate of 12 percent, what is the present value of your winnings?
Answer: (It is an annuity of 50’000 each year for 20 years)
Exercise 3
Rusty Steele will receive an annuity of $10,000 for the next 10 years; at the end of the next three years (that is year 11, 12, 13) he will get the following payments: $4,000, $7,000, and $9,000. At a discount rate of 10 percent, what is the present value of all future benefits?
Answer: In this case we have an annuity of 10000 for 10 years and then 3 single cash flows of 4000, 7000, and 9000 for years 11, 12 and 13. First we find the present value of the annuity:
Then we find the present value of the other three cash flows:
Then we sum PV with PV(11), PV(12) and PV(13).
Exercise 4
(Amortized loan) Your aunt borrows $50,000 from the bank at 10% interest for 8 years. What equal annual payments must be made to discharge the loan, plus pay the bank its required rate of interest (round to the nearest dollar)? How much of his first payment will be applied to interest? To principal? How much of her second payment will be applied to each?
Answer: The amount borrowed is the present value of an annuity. We need to find the payments of this annuity which correspond to the installments of the loan.
So,
= 9372
Beginning loan balance
PMT
Interest
Principal reduction (PMT – interest)
Loan ending balance = Beg. Balance – loan reduction
50000
9372
5000 (50000*0.1)
9372-5000=4372
50000-4372=45628
45628
9372
4562.8