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
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?
=1.05 * 0.93 * 1.06
= 1.035 This means 3.5% increase.
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
You should notice:
$140,000 to pay off in ten years
5.5% annual interest
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
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.
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.
$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%.
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: that compounds quarterly at an annual interest rate of 4.7%?
Activities 13 and 14