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# Calculating PV, FV, periods and rate of interest

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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%

#### 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.

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