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# Applied 40S May 7, 2009

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The Rule of 72, nominal vrs effective interest rates.

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### Applied 40S May 7, 2009

1. 1. Credit Cards and Interest Rates current Canadian rates My favorite Credit Card by ﬂickr user .KM.
2. 2. Solve for FV (the future value) ... 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? HOMEWORK N= I%= PV= PMT= FV= P/Y= C/Y= PMT: END BEGIN
3. 3. HOMEWORK Watching Money Grow ... N= Calculate the ﬁnal balance I%= if \$7500 were invested at PV= 8% per year, compounded PMT= semi-annually 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 N= Calculate the ﬁnal balance if \$1500 were I%= invested at 8% per year, compounded semi- PV= annually, with additional investments of \$1 000 PMT= at the end of every six months for ﬁve years. 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 3-month period? PMT= FV= P/Y= C/Y= PMT: END BEGIN
5. 5. 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 2: \$100/month Option 1: \$1200/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
6. 6. 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
7. 7. 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
8. 8. Scenario 1: You have an investment that compounds annually at 7%. How long will it take to double? Scenario 2: You are shopping for an investment that will double in 6 years. What interest rate are you looking for?
9. 9. Use the Rule of 72 to estimate the doubling time for these interest rates: (c) 24% per annum, (b) 8% per annum, (a) 4% 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?
10. 10. Understanding Credit Card Interest Rates or The Difference Between Nominal and Effective Interest Rates Credit Cards by ﬂickr user Andres Rueda
11. 11. Nominal vrs. Effective Interest Rate You have money to invest in interest-earning 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
12. 12. 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.
13. 13. HOMEWORK Marge invested \$2500 at 6.5% per annum N= compounded quarterly. Calculate the value I%= of her investment after three years. 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
14. 14. HOMEWORK Credit Card Interest 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
15. 15. 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- HOMEWORK annually. 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?