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)
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
= $5000(1 +
= $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.
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.
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
$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)