Economics of Engineering - PowerPoint Presentation

Slide1

Economics of Engineering

Day 2

http://fairway.ecn.purdue.edu

/~

step/class_material

Installment Loans

Up to this point, we have simply talked

about taking

a loan from the bank and repaying it back as one lump sum. What about repaying the loan using installment payments?

Will the loan cost you more or less

?

Why?

Revisiting a previous problem

You have to borrow $1000 from the bank and will pay it back in 5 years at 12% compounded monthly

.

Or, in other words you borrowed $1000 and 5 years later you paid the bank back $1000 plus you gave them

______ in

interest.

Installment Loans

Another way to retire debt is by making periodic payments instead

of a

single large payment at the end of a given time period.

This

payment

process is used by most companies, if a large sum of cash is needed to start a new venture.

You can determine the periodic payment by:

Where:

A = periodic payment

P = principal amount

i = interest rate

n = number of payment periods

Installment Loans continued

You have to borrow $1000 from the bank at

12% compounded monthly

and you will pay it back over

5 years by making equal monthly payments

.

Installment Loans

continued

Or, in other

words,

you

borrow

$

1000,

and

then every

month, for 5 years, you

pay

the bank $22.24. Thus at the end of 60 payments (59 of $22.24 and 1 of $22.51 at the end) you have paid the bank back $1000 plus you gave them $334.67 in interest.

Team Exercise

As a TEAM: You will have 5 minutes to work the following problem using Excel.

Your

worksheet should be formatted as shown.

You decide to purchase a pre-owned automobile that has a total cost of $

15,500

. You have $

6,250

in savings, which you have decided to use. The remainder will be borrowed at an interest rate of 8.5% per year, compounded monthly, with monthly payment for 3 years.

Input

Compute

Payment = Interest + Debt Reduction

When you make a constant payment, a portion of the payment is a payment of interest, while another portion of the payment actually goes towards reducing the debt (also known as the principal).

How do you know how much of a payment is reducing your debt versus paying for interest?

Team Exercise

Modify your spreadsheet so you can see how each payment is actually paying off the loan.

Remember each payment pays some of the interest and some of the loan.

What do you need to compute?

This is the payment number (1-36)

This is the amount paid each month (Montly pymts)

This is how of the payment is actually being used to reduce the debt (current payment – interest payment)

This is

the interest payment on the current amount (compound interest rate*Principal remaining)…

recall the compound interest rate is the annual interest rate/number of interest periods.

This is how much debt you still have after the payment.

Getting Started - Amt

Paid Cell

This will be constant.

Initial Principal Remaining Cell

This is what you will owe before you make any payments – the total borrowed

Interest Cell

Note: Interest is calculated based on the total owed, which is different from the principal remaining if and only if you pay less than the interest accumulated each month.

Principal Cell

.

Principal Remaining Cell

Total Interest Cell

Filling in the Table

Highlight the cells in row Payment 1, click and drag downwards

Present Worth

When loaning money, one of the most important things to know is how much your transaction is worth at any given time.

Present worth is a term used to describe the value of your loan.

Present Worth

Proof

F = P(1 +

i

)

n

Then rearrange to get:

→

P = F/(1 +

i

)

n

OR

→

P = F(1 +

i

)

-n

Present WorthExample

What initial investment do you have to make today to be guaranteed to have $12588.15 at the end of 4 years with 12% APY compounded annually?