# Calculating present value and annual payments

1. Calculate the present value of $90,000 to be received 14 years from now if the decision makers opportunity cost 10 percent.

2. Find the present value at 9 percent of each of the following five cash inflow streams. Assume that cash inflows occur at the end of the year.

Year A B

1 $8,000 $10,000

2 9,000 10,000

3 10,000 10,000

4 11,000 10,000

5 12,000 10,000

3. If an individual wishes to accumulate $15,000 in six years by making equal annual end of year deposits into an account paying 7 percent interest, how large should the deposit be?

4. A lender wishes to to determine the size of the equal annual end of year payments necessary to fully amortize a $40,000 loan at 11 percent interest over three years. How large should the payments be?

#### Solution Preview

1. Calculate the present value of $90,000 to be received 14 years from now if the decision makers opportunity cost 10 percent.

Future Value=FV=$90000

Number of periods=n=14

Opportunity cost=r=10%

Present Value=PV=FV/(1+r)^n=90000/(1+10%)^14=23699.81

2. Find the present value at 9 percent of each of the following five cash inflow streams. Assume that cash inflows occur at the end of the year.

year A B

1 $8,000 ...

#### Solution Summary

There are four problems. Solutions to first two problems depict the steps to calculate present value of the given cash flows. Solutions to another two problems explain the methodology to calculate annual year end payments to meet the given financial objective.