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# Financial Mathematics II - PowerPoint PPT Presentation

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. Three Review Questions. 1. Successive Percents

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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.

### Three Review Questions

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

### This week’s topics

• Loans

• Mortgage/School loans

• Credit Card Debts

### Loans

• 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

### Loans

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.

### Creating an amortization table

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

### Creating an amortization table

Example 1

Our scenario:

\$140,000 to pay off in ten years

5.5% annual interest

### Creating an amortization table

• 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.

### Creating an amortization table

• 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

### Creating an amortization table

• Fill in as follows:

monthly interest

annual interest / 12 months

10 years * 12 months/year

negative sign necessary!

### Creating an amortization table

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

beginning balance * interest rate / 12

### Creating an amortization table

For the principal, we want to use the formula:

payment – interest

### Creating an amortization table

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

month 1 beg balance – principal paid

### Creating an amortization table

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

### Creating an amortization table

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

### Creating an amortization table

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

### Creating an amortization table

what you paid altogether

what you originally borrowed

what you paid in interest

### Creating an amortization table

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.

### Creating an amortization table

Example 2

Our scenario:

\$350,000 house.

\$50,000 down payment.

5.8% annual interest.

Pay off in 30 years.

### Credit Card Debts

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%.

### Credit Card Scenarios

• 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.

### Credit Card Scenarios

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?

### Credit Card Scenarios

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?

### Credit Card Scenarios

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