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Financial Mathematics II

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Financial Mathematics II

Week 9

- Work on stage 3 of final project this week.
- Paper copy is due next week (include all stages, including before and after revisions).
- Presentation is due next week.

1. Successive Percents

If your portfolio performed well one year and had a 5% increase, and the following year performed poorly and had a 7% decrease, and then did well again the year after that and had a 6% increase, how did the portfolio perform altogether for the three years?

(1+0.05)(1-0.07)(1+0.06)

=1.05 * 0.93 * 1.06

= 1.035 This means 3.5% increase.

2. Savings Account

How much do you need to deposit into a savings account that compounds monthly at 3.5% annual interest if you want to save up $5,000 in 10 years?

3. What is the annual percentage yield for a savings account that compounds quarterly at an annual interest rate of 4.7%?

Let’s use $1,000 as the principal.

After one year, we’ll have

Percent change for one year (APY) is

- Loans
- Mortgage/School loans

- Credit Card Debts

- Our goals for this lesson:
- To work with fixed rate, fixed duration loans.
- To calculate monthly payments.
- To be able to calculate how much total interest is paid for a loan.

- Excel skills needed:
- Create amortization tables using the PMT function

You should notice:

- Payments are the same from month to month.
- Your initial payments mainly go into paying off the interest. Towards the end, your monthly payments mainly go into paying off the principal.
- The longer you choose to pay off your loans, the more you end up paying. Sometimes even 2 or 3 times what you initially borrowed.

- A table that lets you see your schedule to pay off the loan.

Example 1

Our scenario:

$140,000 to pay off in ten years

5.5% annual interest

- Fill in headings across in the first row.
- Fill in the months column. Start at 0.
- Type in loan amount ($140,000) as the end balance of month 0.

- Fill in formulas for month 1.
Beg balance = end balance of month

(Don’t just type it in)

For payments, use the PMT function. You can access the PMT function by pressing

- choose PMT

- Fill in as follows:

monthly interest

annual interest / 12 months

10 years * 12 months/year

negative sign necessary!

For the interest for month one, we want the formula:

beginning balance * interest rate / 12

For the principal, we want to use the formula:

payment – interest

Finally, the end balance for the first month uses the following formula:

month 1 beg balance – principal paid

5. Drag down the entire row until the end balance is zero. In this case, 120 months.

- Notice the difference between the first payments and the last payments

Let’s look at what we’ve paid in interest and what we’ve paid in total after the ten years.

press the auto sum button

what you paid altogether

what you originally borrowed

what you paid in interest

What is the percent of the original amount borrowed is the total interest paid?

So 5.5% interest does not mean you pay 5.5% of the total as interest.

Example 2

Our scenario:

$350,000 house.

$50,000 down payment.

5.8% annual interest.

Pay off in 30 years.

Credit card debts are scary because they accrue interests at much higher rates.

The average interest rate is15%, but it can go as high as 30%.

- If someone has a $5,000 credit card debt, how much interest would have to be paid on the debt the first month? Assume 30% interest.

2a. John has $50,000 in credit card debt. If he’s planning to pay $1,200 every month, what would be his balance in five years? Assume an interest rate of 20%.

2b. How much interest in total does he pay after 5 years?

3a. Suppose you’ve accumulated $4,000 on your credit card at an interest rate of 18%. Minimum payment option is 2% per month (not less than $25). When will you pay it all off?

3b. How much would you have paid by the end? How much in interest?

4. Jane wants to pay off her $8,000 credit card debt in 9 years. Using the PMT function, determine her monthly payment assuming she’ll make equal payments for 9 years. Assume 11% APR.

Today:

Activities 13 and 14