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# Lesson 2 Apr 6 2010

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### Lesson 2 Apr 6 2010

1. 1. Interest Rates
2. 2. Solve for FV (the future value) ... HOMEWORK You decide to invest \$6500. The bank offers an interest rate of  8.25% compounded annually. What will your money be worth in 7  years if the interest rate remains unchanged? N= I%= PV= PMT= FV= P/Y= C/Y= PMT: END   BEGIN
3. 3. Watching Money Grow ... HOMEWORK N= Calculate the final balance  I%= if \$7500 were invested at  PV= 8% per year, compounded  PMT= semi­annually for 6 years. FV= P/Y= C/Y= PMT: END   BEGIN How long will it take \$12 000  N= invested at 7.2% per year,  I%= compounded quarterly, to  PV= grow to \$15 000? PMT= FV= P/Y= C/Y= PMT: END   BEGIN
4. 4. Investing Regularly ... HOMEWORK Calculate the final balance if \$1500 were  N= invested at 8% per year, compounded semi­ I%= annually, with additional investments of \$1 000   PV= at the end of every six months for five years. PMT= FV= P/Y= C/Y= PMT: END   BEGIN How long will it take to save \$35 000, if \$2 500  N= were invested at 7.2% per year, compounded  I%= quarterly, followed by an additional \$400 at the  PV= end of each 3­month period?  PMT= FV= P/Y= C/Y= PMT: END   BEGIN
5. 5. Imagine that you have just won \$500000.00 in a contest.  You invest it as 12% compounded semi­annually.  \$30088.68 You decide to live off the investment.  Determine how much money you can withdraw each compounding  period if you want the money to last 50 years. N= I%= PV= PMT= FV= P/Y= C/Y= PMT: END   BEGIN
6. 6. Investing Frequently ... A financial institution offers an annual interest rate of 6%,  compounded monthly. Compare \$1200 invested at the end of each year to \$100 invested  at the end of each month. Option 1: \$1200/year Option 2: \$100/month N= N= I%= I%= PV= PV= PMT= PMT= FV= FV= P/Y= P/Y= C/Y= C/Y= PMT: END   BEGIN PMT: END   BEGIN
7. 7. Doubling Our Money ... \$1200 is invested at 6% interest compounded annually. How long  will it take to double? N= N= I%= I%= PV= PV= PMT= PMT= FV= FV= P/Y= P/Y= C/Y= C/Y= PMT: END   BEGIN PMT: END   BEGIN
8. 8. The Rule of 72 Here's a handy way to figure out how long your investment will take to  double in value. It is called the Rule of 72. (Interest Rate %) x (Years to Double) = 72 To find the number of years given a percentage: Years =           72 (Interest Rate %) To find the percentage required to double given the years: Rate =       72 Years Numbers 72 by flickr user szczel
9. 9. Example 1: You have an investment that compounds annually at 7%.  How long will it take to double? Example 2: You are shopping for an investment that will double in 6  years. What interest rate are you looking for?
10. 10. Use the Rule of 72 to estimate the doubling time for these interest rates: (a) 4% per annum,  (b) 8% per annum,  (c) 24% per annum,  compounded annually compounded annually compounded annually Use the TVM solver in your calculator to calculate the the compound  amount of a \$100 investment for the doubling times estimated above. N= N= N= I%= I%= I%= PV= PV= PV= PMT= PMT= PMT= FV= FV= FV= P/Y= P/Y= P/Y= C/Y= C/Y= C/Y= PMT: END   BEGIN PMT: END   BEGIN PMT: END   BEGIN How accurate does the Rule of 72 seem to be?
11. 11. Understanding Credit  Card Interest Rates or The Difference Between  Nominal and  Effective Interest Rates Credit Cards by flickr user Andres Rueda
12. 12. Nominal vrs. Effective Interest Rate You have money to invest in interest­earning deposits.  You have  determined that suitable deposits are available at your bank paying  6.5% per annum compounded annually, at a local trust company paying  6.4% per annum compounded monthly and at the Student Credit Union  paying 6.45% per annum compounded semiannually.  Which institution  offers the best rate of interest? N= N= N= I%= I%= I%= PV= PV= PV= PMT= PMT= PMT= FV= FV= FV= P/Y= P/Y= P/Y= C/Y= C/Y= C/Y= PMT: END   BEGIN PMT: END   BEGIN PMT: END   BEGIN
13. 13. Nominal Rate of Interest ­  The stated rate of interest applied to your  investment. 6.5% per annum       compounded semiannually 6.4% per annum       compounded annually  6.45% per annum     compounded monthly Effective Rate of Interest ­ The interest rate if an annuity is  compounded annually.
14. 14. Marge invested \$2500 at 6.5% per annum  HOMEWORK compounded quarterly. Calculate the value  N= of her investment after three years. I%= PV= PMT= FV= P/Y= C/Y= PMT: END   BEGIN Calculate the effective interest rate. N= I%= PV= PMT= FV= P/Y= C/Y= PMT: END   BEGIN
15. 15. Credit Card Interest HOMEWORK Calculate the effective interest rate of \$1.00 invested at 18.5%  compounded daily for one year. N= N= I%= I%= PV= PV= PMT= PMT= FV= FV= P/Y= P/Y= C/Y= C/Y= PMT: END   BEGIN PMT: END   BEGIN
16. 16. Shaina wishes to invest \$2000 given by her grandfather. She has an  option of a guaranteed investment certificate earning 8.85%,  compounded quarterly, or a savings bond of 9%, compounded semi­ annually. HOMEWORK Which investment  N= N= should she choose? I%= I%= PV= PV= PMT= PMT= FV= FV= P/Y= P/Y= C/Y= C/Y= PMT: END   BEGIN PMT: END   BEGIN If each investment term is 5 years, what will be the difference in  their values at the end of the term?