Amortized Loans

Section 5.4


Amortized Loan: A loan for which the loan amount plus interest owed is paid off in a series of regular equal payments.

Previously, add-on interest loans were a type of amortized loans.

The difference is the amount of interest paid.

An amortized loan can be viewed as the FV of an ordinary annuity.

        FV (annuity) = FV (amortized loan)



Example 1: 

What is a better deal?  Borrowing $5000 for one year @ 10% simple interest amortized or add-on interest?  What is the monthly payment of each?

Simple interest Amortized:  


        pymt = $439.58


Add-on Loan: 

        pymt =      FV          =    $5000(1 + (0.1)(1))  
                     # of pymts                   12

        = $5500/12 = $458.33


The better deal is the amortized loan.

Why are the payments less with an amortized loan?  The add-on interest loan calculates interest on the initial amount $5000 for the entire length of the loan.  The simple interest amortized loan calculates interest on the balance of the loan after each payment so the interest decreases.


Example 2: 

Set up amortization table for the 1st three months of payments for the better deal.  We know the payments are $439.58.

        1st payment: I = Prt                

        $5000(.1)(1/12) = $41.67 interest

        $439.58 41.67 = $397.91 Principal paid

        $5000 397.91 = $4602.09 new balance


Finding unpaid balance: 

        Current value of loan Current value of annuity


        Unpaid Balance = P(1 + i)n  - Pymt(1 + i)n 1

In this case n represents the number of payments already made.


Example 3:  

Find the unpaid balance on the loan in EX 2 after 6 months.

        n = 6

        Unpaid balance = $5000(1 + .1/12)6 - $439.58(1 + .1/12)6


        $5255.27 $2693.04 = $2562.23

How much do you save by paying off early?  If we continue to make payments

        6(439.58) = $2637.48 2562.23 = $75.28 interest




Review for Exam #1


Dimensional Analysis: Converting units of measurement


Perimeter (Circumference of Circles) and Area: One-dimensional and two-dimensional measurements of figures; Quadrilaterals, Triangles, Circles.


Right Triangle Trigonometry: Special Triangles; 45*, 30-60-90*.

Trig Ratios: Sine, Cosine, Tangent.

Finding angle q  by Arcsine, Arccosine, Arctangent


Simple Interest and Future Value (FV) Add-on Interest, Finance charges,

Average Daily Balance (ADB)


Compound Interest and FV

Annual Yield, Periodic Rate


Annuities and FV, Payment Period, Term,

Ordinary  Annuity , Tax-Deferred Annuity (TDA)


Amortized Loans and FV



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