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:

n

n

i 1+iA=P

(1+i) -1

Where:A = periodic paymentP = principal amounti = interest raten = 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.

24.22$

112

%121

12

%121

12

%12

1000$ 60

60

A

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 ExerciseAs 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 ExerciseModify 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 CellThis 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?