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?

5000 5000  

P

 

P

1  .035

12  1.002917

 12*10  120 5000 

P

 1.418345



P

 $3525.24

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 .047

 4*1

A

  1000 1   1047.83

4 Percent change for one year (APY) is  .047834

 4.78%

APY

1000

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

Creating an amortization table Example 1 Our scenario: $140,000 to pay off in ten years 5.5% annual interest

Creating an amortization table 1. Fill in headings across in the first row. 2. Fill in the months column. Start at 0.

3. Type in loan amount ($140,000) as the end balance of month 0.

Creating an amortization table 4. 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

Creating an amortization table • 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?

42324.15

 .3023

 30.23% 140000 So 5.5% interest

does not

of the total as interest. mean you pay 5.5%

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 1. 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