Math 1140 Financial Mathematics

Lecture 4More Simple

Interest

Ana Nora Evans403 KerchofAnaNEvans@virginia.eduhttp://people.virginia.edu/~ans5k/

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Homework 2

Turn in homework 2 now!

I mean it!

I will not accept it later!

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Questions?

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Homework 2

If a cycle contains a single charge denoted by C made on the first day of the cycle then the average daily balance and daily accrual give the same interest.

Average Daily Balance: ADB = C * 30 / 30 = CInterest = ADB * cycle length * APR/365 = C * 30 * APR/365Daily Balance: DB = C Interest per day = C * APR/365Interest = 30 * C * APR/365

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Homework 2

If a cycle contains a single charge denoted by C made on the last day of the cycle then the average daily balance and daily accrual give the same interest.

Average Daily Balance: ADB = C / 30 Interest = ADB * cycle length * APR/365 = (C /30) * 30 * APR/365 = C * APR/365Daily Balance: DB = 0 for all the days except last, which is CInterest for the last day = C * APR/365Interest = C * APR/365

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Homework 2

If a cycle contains a single charge then the average daily balance and daily accrual give the same interest.

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Trust your intuition, but verify

Your intuition says it is better to pay a smaller interest rate.

The difference in interest paid with average daily balance and daily accrual is pennies on the dollar. (assuming the same interest rate)

The interest rates in the two methods differ by a factor of 2.

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Do not confuse average daily balance with two-cycle average daily balance.

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Terms from last time

Exact timeApproximate timeOrdinary interestExact interestBanker’s Rule

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More practice

Next homework!

The odd number exercises from the textbook!

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Add-on Loan

You purchase for $2,150 a 2000 Chevy Cavalier from friendly local dealer Defective Motors. He will finance your loan for two years, charging you 11% add-on interest on the loan. How much is your monthly payment?

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Solution

Step 1 – calculate the maturity value of the loan

Step 2 – calculate the monthly payments

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Thinking TimeIs this the same as a simple interest

loan?A) YesB) NoC) MaybeD) I was napping for the last 10

minutes or more

This is a participation question.

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Discussion

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Even more thinkingThe value of the money I pay for a six months

add-on loan compared with a simple interest loan paid at maturity is:

A) BiggerB) SmallerC) Exactly the sameD) I would like to go back to sleepThis is a participation question.

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Discussion

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It’s legal!

This type of financing is offered in in-store loans from appliance, furniture, and auto dealers.

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Break

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Prompt Payment Discount

Discount offered for quick cash payments.Example: some medical bills, building

constructors bills.Notation: 2/10 n/45If the balance is paid in 10 days then there is a

2% discount. The full balance (net) is due in 45 days.

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Example

Nora has to pay a $4,500 bill to her dentist. If she pays cash on the day of the service she gets a 5% discount. The full payment is due in 30 days. Assume she keeps the money in a savings account offering 2% simple interest rate.

When should she pay?

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Prompt Payment

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Payment at the Deadline

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Which method is better?

What interest rate would make it at least as good to pay later?

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Real life may be more complicated

Dental insurance!

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Next time

Partial PaymentsStart Discount Interest

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Charge

Due Friday:Read sections 1.8, 1.9

Due Next Wednesday :Third homework