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

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

i

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
.1/12

Owe:

\$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

6.1

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

6.5

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

Trig Ratios: Sine, Cosine, Tangent.

Finding angle q  by Arcsine, Arccosine, Arctangent

5.1

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

5.2

Compound Interest and FV

Annual Yield, Periodic Rate

5.3

Annuities and FV, Payment Period, Term,

Ordinary  Annuity , Tax-Deferred Annuity (TDA)

5.4

Amortized Loans and FV

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