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Calculating PV, FV, periods and rate of interest

Problems:

1.Given the following data, solve for the number of years in each case. (Use a financial calculator).

Present Value Interest rate Future Value Years
$1,200 8% $2,590.71
$16,310 12% $20,459.26
$75,000 3% $182,044.69
$183,650 9% $308,000

2.You expect your newly born child to attend college in 18 years. You have $12,000 to set aside for that purpose.
You also expect that the total cost of college education to be $100,000 by that time.

Calculate the interest rate at which you have to invest today to achieve your goal.

3.How long does it take to double your money at 9% interest rate?

4.How long does it take to triple your money at 9% interest rate?

5.Great Lakes Inc. has an unfunded pension liability of $300 million that must be paid in 18 years. The financial analyst wants to discount this liability back to, present for valuation purposes.

The appropriate discount rate is 8%.

What is the present value of this liability?

6.Highlight Inc. is considering an investment project with the following cash flows:

YEAR Cash Flow
1 $300
2 $400
3 $600
4 $900

If the discount rate is 10% , calculate the present value of these cash flows
What will be the present value if the discount rate is changed to 15%

7.Solarlight Inc. is considering a project with the following cash flows :
YEAR Cash Flow
1 $800
2 $700
3 $600
4 $500

Calculate the future value of these cash flows in year 4., if the interest rate is 12%
What will be the present value if the interest rate is changed to 16%?

8.Newsys Inc. will generate $30,000 per year for the next five years from a new database system. The system requires an investment of 120,000 today. If the opportunity cost of funds is 6%, is the system worth installing?

9.An investment pays $2,000 per year for 10 years. The payments occur at the end of each year The required rate of return in 12%.

Calculate the value of the investment today.
What will be its value if the payments occurred at the beginning of each year?

10.If Mr. Hobbit deposits $2,000 at the end of each year for the next 10 years at an interest rate of 12% per year, how much will be have accumulated? How much will he have accumulated if he deposited the amounts at the beginning of each year?

11.Find the present value of a perpetuity that pays $2,000 per year and the interest rate is 10%

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Solutions:

1.Given the following data, solve for the number of years in each case. (Use a financial calculator).

Present Value Interest rate Future Value Years
$1,200 8% $2,590.71 10
$16,310 12% $20,459.26 2
$75,000 3% $182,044.69 30
$183,650 9% $308,000 6

2.You expect your newly born child to attend college in 18 years. You have $12,000 to set aside for that purpose.
You also expect that the total cost of college education to be $100,000 by that time.

Calculate the interest rate at which you have to invest today to achieve your goal.
Solution:
We are given FV=100,000
PV =12000
n = 18
r =?
We know FV=PV(1+r)^n
100000=12000*(1+r)^18
(8.33333)^(1/18)=1+r
r=12.5011%

3.How long does it take to double your money at 9% interest rate?
Here we have FV/PV =2
So, 2=(1+009)^n
n = ln(2)/ln(1.09)=8.04 years

4.How long does it take to triple your money at 9% interest rate?
FV/PV =3
3=(1+0.09)^n
n=ln(3)/ln(1.09)=12.75 years

5.Great Lakes Inc. has an unfunded pension liability of $300 million that must be paid in 18 years. The financial ...

Solution Summary

There are 11 problems. Solution describes the steps to calculate present value, future value, periods and rate of interest in given situations.

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