# 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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#### Solution Preview

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.

Corporate finance : Time value of money

13. The future value of $200 received today and deposited for three years in an account which pays semiannual interest of 8 percent is ______.

A. $253.00

B. $252.00

C. $158.00

D. $134.66

14. The future value of $100 received today and deposited at 6 percent for four years is

A. $126.

B. $ 79.

C. $124.

D. $116.

15-19. Calculate the present value of the annuity assuming that it is an ordinary annuity.

Case Amount of Annuity Interest Rate Period / Years

A $14,000 9% 3

B $17,500 13% 15

C $975 18% 7

D $1,127,000 4% 9

E $10,000 7% 3

20-24. For each of the cases shown below in the table, calculate the present value of the cash flow:

Case Single Cash Flow Interest Rate End of Periods / Years

A $13,000 10% 5

B $34,000 17% 25

C $16,000 6% 18

D $210,000 15% 15

E $90,000 20% 9

25-29 For each of the cases shown below in the table, calculate the future value of the cash flow:

Case Single Cash Flow Interest Rate End of Periods / Years

A $3,000 10% 7

B $44,000 12% 5

C $6,000 8% 10

D $27,000 16% 12

E $99,000 20% 6

Calculate the above future values in questions 25-29 as semi annual and quarterly compounding.

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