math 1140 financial mathematics lecture 4 more simple interest ana nora evans 403 kerchof...
TRANSCRIPT
![Page 1: Math 1140 Financial Mathematics Lecture 4 More Simple Interest Ana Nora Evans 403 Kerchof AnaNEvans@virginia.edu ans5k](https://reader036.vdocument.in/reader036/viewer/2022062321/56649e045503460f94af08de/html5/thumbnails/1.jpg)
Math 1140 Financial Mathematics
Lecture 4More Simple
Interest
Ana Nora Evans403 [email protected]://people.virginia.edu/~ans5k/
![Page 2: Math 1140 Financial Mathematics Lecture 4 More Simple Interest Ana Nora Evans 403 Kerchof AnaNEvans@virginia.edu ans5k](https://reader036.vdocument.in/reader036/viewer/2022062321/56649e045503460f94af08de/html5/thumbnails/2.jpg)
2Math 1140 - Financial Mathematics
Homework 2
Turn in homework 2 now!
I mean it!
I will not accept it later!
![Page 3: Math 1140 Financial Mathematics Lecture 4 More Simple Interest Ana Nora Evans 403 Kerchof AnaNEvans@virginia.edu ans5k](https://reader036.vdocument.in/reader036/viewer/2022062321/56649e045503460f94af08de/html5/thumbnails/3.jpg)
3Math 1140 - Financial Mathematics
Questions?
![Page 4: Math 1140 Financial Mathematics Lecture 4 More Simple Interest Ana Nora Evans 403 Kerchof AnaNEvans@virginia.edu ans5k](https://reader036.vdocument.in/reader036/viewer/2022062321/56649e045503460f94af08de/html5/thumbnails/4.jpg)
4Math 1140 - Financial Mathematics
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
![Page 5: Math 1140 Financial Mathematics Lecture 4 More Simple Interest Ana Nora Evans 403 Kerchof AnaNEvans@virginia.edu ans5k](https://reader036.vdocument.in/reader036/viewer/2022062321/56649e045503460f94af08de/html5/thumbnails/5.jpg)
5Math 1140 - Financial Mathematics
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
![Page 6: Math 1140 Financial Mathematics Lecture 4 More Simple Interest Ana Nora Evans 403 Kerchof AnaNEvans@virginia.edu ans5k](https://reader036.vdocument.in/reader036/viewer/2022062321/56649e045503460f94af08de/html5/thumbnails/6.jpg)
6Math 1140 - Financial Mathematics
Homework 2
If a cycle contains a single charge then the average daily balance and daily accrual give the same interest.
![Page 7: Math 1140 Financial Mathematics Lecture 4 More Simple Interest Ana Nora Evans 403 Kerchof AnaNEvans@virginia.edu ans5k](https://reader036.vdocument.in/reader036/viewer/2022062321/56649e045503460f94af08de/html5/thumbnails/7.jpg)
7Math 1140 - Financial Mathematics
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.
![Page 8: Math 1140 Financial Mathematics Lecture 4 More Simple Interest Ana Nora Evans 403 Kerchof AnaNEvans@virginia.edu ans5k](https://reader036.vdocument.in/reader036/viewer/2022062321/56649e045503460f94af08de/html5/thumbnails/8.jpg)
8Math 1140 - Financial Mathematics
Do not confuse average daily balance with two-cycle average daily balance.
![Page 9: Math 1140 Financial Mathematics Lecture 4 More Simple Interest Ana Nora Evans 403 Kerchof AnaNEvans@virginia.edu ans5k](https://reader036.vdocument.in/reader036/viewer/2022062321/56649e045503460f94af08de/html5/thumbnails/9.jpg)
9Math 1140 - Financial Mathematics
![Page 10: Math 1140 Financial Mathematics Lecture 4 More Simple Interest Ana Nora Evans 403 Kerchof AnaNEvans@virginia.edu ans5k](https://reader036.vdocument.in/reader036/viewer/2022062321/56649e045503460f94af08de/html5/thumbnails/10.jpg)
10Math 1140 - Financial Mathematics
Terms from last time
Exact timeApproximate timeOrdinary interestExact interestBanker’s Rule
![Page 11: Math 1140 Financial Mathematics Lecture 4 More Simple Interest Ana Nora Evans 403 Kerchof AnaNEvans@virginia.edu ans5k](https://reader036.vdocument.in/reader036/viewer/2022062321/56649e045503460f94af08de/html5/thumbnails/11.jpg)
11Math 1140 - Financial Mathematics
More practice
Next homework!
The odd number exercises from the textbook!
![Page 12: Math 1140 Financial Mathematics Lecture 4 More Simple Interest Ana Nora Evans 403 Kerchof AnaNEvans@virginia.edu ans5k](https://reader036.vdocument.in/reader036/viewer/2022062321/56649e045503460f94af08de/html5/thumbnails/12.jpg)
12Math 1140 - Financial Mathematics
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?
![Page 13: Math 1140 Financial Mathematics Lecture 4 More Simple Interest Ana Nora Evans 403 Kerchof AnaNEvans@virginia.edu ans5k](https://reader036.vdocument.in/reader036/viewer/2022062321/56649e045503460f94af08de/html5/thumbnails/13.jpg)
13Math 1140 - Financial Mathematics
Solution
Step 1 – calculate the maturity value of the loan
Step 2 – calculate the monthly payments
![Page 14: Math 1140 Financial Mathematics Lecture 4 More Simple Interest Ana Nora Evans 403 Kerchof AnaNEvans@virginia.edu ans5k](https://reader036.vdocument.in/reader036/viewer/2022062321/56649e045503460f94af08de/html5/thumbnails/14.jpg)
14Math 1140 - Financial Mathematics
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.
![Page 15: Math 1140 Financial Mathematics Lecture 4 More Simple Interest Ana Nora Evans 403 Kerchof AnaNEvans@virginia.edu ans5k](https://reader036.vdocument.in/reader036/viewer/2022062321/56649e045503460f94af08de/html5/thumbnails/15.jpg)
15Math 1140 - Financial Mathematics
Discussion
![Page 16: Math 1140 Financial Mathematics Lecture 4 More Simple Interest Ana Nora Evans 403 Kerchof AnaNEvans@virginia.edu ans5k](https://reader036.vdocument.in/reader036/viewer/2022062321/56649e045503460f94af08de/html5/thumbnails/16.jpg)
16Math 1140 - Financial Mathematics
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.
![Page 17: Math 1140 Financial Mathematics Lecture 4 More Simple Interest Ana Nora Evans 403 Kerchof AnaNEvans@virginia.edu ans5k](https://reader036.vdocument.in/reader036/viewer/2022062321/56649e045503460f94af08de/html5/thumbnails/17.jpg)
17Math 1140 - Financial Mathematics
Discussion
![Page 18: Math 1140 Financial Mathematics Lecture 4 More Simple Interest Ana Nora Evans 403 Kerchof AnaNEvans@virginia.edu ans5k](https://reader036.vdocument.in/reader036/viewer/2022062321/56649e045503460f94af08de/html5/thumbnails/18.jpg)
18Math 1140 - Financial Mathematics
It’s legal!
This type of financing is offered in in-store loans from appliance, furniture, and auto dealers.
![Page 19: Math 1140 Financial Mathematics Lecture 4 More Simple Interest Ana Nora Evans 403 Kerchof AnaNEvans@virginia.edu ans5k](https://reader036.vdocument.in/reader036/viewer/2022062321/56649e045503460f94af08de/html5/thumbnails/19.jpg)
19Math 1140 - Financial Mathematics
Break
![Page 20: Math 1140 Financial Mathematics Lecture 4 More Simple Interest Ana Nora Evans 403 Kerchof AnaNEvans@virginia.edu ans5k](https://reader036.vdocument.in/reader036/viewer/2022062321/56649e045503460f94af08de/html5/thumbnails/20.jpg)
20Math 1140 - Financial Mathematics
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.
![Page 21: Math 1140 Financial Mathematics Lecture 4 More Simple Interest Ana Nora Evans 403 Kerchof AnaNEvans@virginia.edu ans5k](https://reader036.vdocument.in/reader036/viewer/2022062321/56649e045503460f94af08de/html5/thumbnails/21.jpg)
21Math 1140 - Financial Mathematics
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?
![Page 22: Math 1140 Financial Mathematics Lecture 4 More Simple Interest Ana Nora Evans 403 Kerchof AnaNEvans@virginia.edu ans5k](https://reader036.vdocument.in/reader036/viewer/2022062321/56649e045503460f94af08de/html5/thumbnails/22.jpg)
22Math 1140 - Financial Mathematics
Prompt Payment
![Page 23: Math 1140 Financial Mathematics Lecture 4 More Simple Interest Ana Nora Evans 403 Kerchof AnaNEvans@virginia.edu ans5k](https://reader036.vdocument.in/reader036/viewer/2022062321/56649e045503460f94af08de/html5/thumbnails/23.jpg)
23Math 1140 - Financial Mathematics
Payment at the Deadline
![Page 24: Math 1140 Financial Mathematics Lecture 4 More Simple Interest Ana Nora Evans 403 Kerchof AnaNEvans@virginia.edu ans5k](https://reader036.vdocument.in/reader036/viewer/2022062321/56649e045503460f94af08de/html5/thumbnails/24.jpg)
24Math 1140 - Financial Mathematics
Which method is better?
What interest rate would make it at least as good to pay later?
![Page 25: Math 1140 Financial Mathematics Lecture 4 More Simple Interest Ana Nora Evans 403 Kerchof AnaNEvans@virginia.edu ans5k](https://reader036.vdocument.in/reader036/viewer/2022062321/56649e045503460f94af08de/html5/thumbnails/25.jpg)
25Math 1140 - Financial Mathematics
![Page 26: Math 1140 Financial Mathematics Lecture 4 More Simple Interest Ana Nora Evans 403 Kerchof AnaNEvans@virginia.edu ans5k](https://reader036.vdocument.in/reader036/viewer/2022062321/56649e045503460f94af08de/html5/thumbnails/26.jpg)
26Math 1140 - Financial Mathematics
Real life may be more complicated
Dental insurance!
![Page 27: Math 1140 Financial Mathematics Lecture 4 More Simple Interest Ana Nora Evans 403 Kerchof AnaNEvans@virginia.edu ans5k](https://reader036.vdocument.in/reader036/viewer/2022062321/56649e045503460f94af08de/html5/thumbnails/27.jpg)
27Math 1140 - Financial Mathematics
Next time
Partial PaymentsStart Discount Interest
![Page 28: Math 1140 Financial Mathematics Lecture 4 More Simple Interest Ana Nora Evans 403 Kerchof AnaNEvans@virginia.edu ans5k](https://reader036.vdocument.in/reader036/viewer/2022062321/56649e045503460f94af08de/html5/thumbnails/28.jpg)
28Math 1140 - Financial Mathematics
Charge
Due Friday:Read sections 1.8, 1.9
Due Next Wednesday :Third homework