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living with the lab. Engineering Economics - Uniform Series. It is common for equal amounts to be withdrawn or deposited at the end of each period.

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living with the lab

Engineering Economics - Uniform Series

It is common for equal amounts to be withdrawn or deposited at the end of each period.

For example, if you purchase a home with a 30-year loan, it is common to pay the same amount at the end of each month over the entire 30 years.

You would need to pay \$899 per month over 30 years for a \$150,000 home assuming an annual interest rate of 6% compounded monthly.

living with the lab

Example – Savings Account

Consider the cash flow diagram for a savings account where an amount “A” of \$100 is deposited at the end of each year over six years with an annual interest rate of 8% compounded annually. Find the value of the account at the end of six years.

\$100 \$100 \$100 \$100 \$100 \$100

<in>

0 1 2 3 4 5 6

<out>

F

While we can find “F” as shown above, we know there must be an easier way. Next, we will develop an equation for “F” in terms of the periodic amount “A.”

living with the lab

Find F in terms of A

A A A A

0 1 2 3 4

end of year 4:

F

end of year 3:

end of year 2:

+

end of year 1:

Generalizing for n periods . . .

living with the lab

Example: Starting at age 23, a young engineering graduate puts \$500 a month into an investment that earns an average of 8% annually. Assuming monthly compounding and a constant rate of return, determine how much money the old engineer will have at age 73.

A A A A

A A A

0 1 2 3 4

n-2 n-1 n

F

living with the lab

Present Amount for a Uniform Series

The present amount corresponding to uniform periodic payments or receipts can be determined by combining the equations below.

living with the lab

Class Problem

You expect to need a \$2,000 computer in 36 months. How much should you save each month if you would like to pay cash for the computer? Assume 5% annual interest.

You decide to buy the same computer now by getting a loan at 9% interest. You will pay off the loan over the next 36 months in equal payments. How much will you pay per month?

living with the lab

A Few “Fine Points” for Solving Problems

A A A A

A A A

0 1 2 3 4

n-2 n-1 n

F

• When computing F, the uniform amounts “A” come at the end of each period

A A A A

A A A

0 1 2 3 4

n-2 n-1 n

P

• The present amount “P” is computed at time = 0, one interest period before the first installment “A”
• When computing either F or P, the last “A” comes at period n (at the end of the last period)