# Calculating present and future value of single cash flow

Problem 4.4

For each of the cases shown in the following table, calculate the future value of single cash flow deposited today that will be available at the end of the deposit period if the interest is compounded annually at the rate specified over the given period.

Case Single Cash Flow Interest Rate Deposit period (years)

A $200 5% 20

B 4500 8 7

C 10000 9 10

D 25000 10 12

E 37000 11 5

F 40000 12 9

Problem 4.5

You have $1500 to invest today at 7% interest compounded annually.

a. Find how much you will have accumulated in the account at the end of

(1)3 years, (2) 6 years, and (3) 9 years

b. Use your findings in part a to calculate the amount of interest earned in

(1)The first 3 years (years 1 to 3), (2) the second 3 years (years 4 to 6), and (3) the third 3 years (years 7 to 9)

c. Compare and contrast your findings in part b. Explain why the amount of interest earned increase in each succeeding 3-year period.

Problem 4.6

As part of your financing planning, you wish to purchase a new car exactly 5 years from today. The car you wish to purchase costs $14,000 today, and your research indicates that price will increase by 2% to 4% per year over the next 5 years.

a. Estimate the price of the car at the end of 5 years if inflation is (1) 2% per year and (2) 4% per year.

b. How much more expansive will the car be if the rate of inflation is 4% rather than 2%

#### Solution Preview

P4-4

Case A

Present Value of Cash flow=PV=$200

Interest Rate=i=5%

Number of periods=20

Future value of deposit=FV=PV*(1+i)^n=200*(1+5%)^20=$530.66

Case B

Present Value of Cash flow=PV=$4500

Interest Rate=i=8%

Number of periods=7

Future value of deposit=FV=PV*(1+i)^n=4500*(1+8%)^7=$7712.21

Case C

Present Value of Cash flow=PV=$10000

Interest Rate=i=9%

Number of periods=10

Future value of deposit=FV=PV*(1+i)^n=10000*(1+9%)^10=$23673.64

Case D

Present Value of Cash flow=PV=$25000

Interest ...

#### Solution Summary

There are three problems. Solutions to these problems provide step by step methodology to calculate present value, interest earned and future value of single cash flow.