Compound Interest Lesson 7 PDF

Week 8 Lesson 7: The Difference Between Simple Interest and Compound Interest - Answers Example: investment of \$1000 for 3 years Simple interest: use 5% simple interest as the interest rate Use the same example -- compound interest - at 5% compounded annually. FV = PV(1+ *i*)^N^ = 1000(1+.05)^3...

Week 8 Lesson 7: The Difference Between Simple Interest and Compound Interest - Answers Example: investment of \$1000 for 3 years Simple interest: use 5% simple interest as the interest rate Use the same example -- compound interest - at 5% compounded annually. FV = PV(1+ *i*)^N^ = 1000(1+.05)^3^ = \$1157.63 I/Y = interest per year (5%=.05) C/Y = compounding per year (annual = 1 time per year) N = \# of compounding periods = \#years\*compounding per year = Y\*C/Y *i* = interest per compounding period (.05/1 =.05) FV = PV(1+ *i*)^N^ = 1000(1+.05)^3^ = \$1157.63 Interest = FV -- PV = 1157.63 -- 1000 = \$157.63 Same example at 5% compounded semi-annually. I/Y interest per year (.05) C/Y = compounding per year (semi-annual = 2 times per year) *i* interest per compounding period =.05/2=.025 AKA: the periodic interest rate N \# of compounding periods = \#years\*compounding per year = 3\*2 = 6 FV = 1000(1+.05/2)^6^ = \$1159.69 Interest = FV -- PV = 1157.63 -- 1000 = \$157.83 Annual C/Y = 1 Semi-annual C/Y = 2 Quarterly C/Y = 4 Monthly C/Y = 12 Daily C/Y = 365 9.1 Basic Concepts 9.4 Using Financial Calculators Using the BA11+ BAII Plus Calculator Start in the top row: CPT compute QUIT over CPT ENTER ↑ ↓ arrows up & down 2^nd^ row: 2ND 3^rd^ row: N \#years\*compounding per year= Y\*C/Y I/Y interest per year P/Y payments per year (over the I/Y) PV present value PMT payment made at regular intervals FV future value +\|- bottom row, on the right For the last example: N = 6: 6 and then N; you will see N = 6 in your display I/Y = 5: 5 and then IY; you will see IY = 5 in your display PV = -1000: 1000 and then +\|- (bottom row, right) C/Y = compounding per year (2 for semi-annual) You do not see C/Y, but we can use P/Y to find it. P/Y = 2. Since we do not have a PMT yet, P/Y = C/Y. For semi-annual compounding C/Y = P/Y = 2. To enter P/Y &↓ C/Y: 2^nd^ P/Y (over I/Y). You will see P/Y = (1,2,4,12). This needs to be a 2. So, 2 ENTER (top row, 2^nd^ button). Use P/Y & ↓ to find C/Y which will be the same as P/Y. You must save this by: 2^nd^ Quit. Summary of the steps: 2^nd^ P/Y 2 Enter 2^nd^ Quit PMT = 0: 0 and then PMT; -- you will see PMT = 0 in your display You do not have a PMT at this time (it will come later) so we need to enter a 0 for PMT Next, CPT FV. The display will show 1159.69 Interest = FV -- PV = 1159.69 -- 1000 = 159.69 9.2 FUTURE VALUE (or Maturity Value) \#1 *If you invested \$5,000 for 10 years at 9% compounded quarterly, how much money would you have in the account at the end of 10 years?* (\$12,175.94) \#2 *If you invested \$10,000 for 4 years at 3% compounded monthly, how much money would you have in the account at the end of 4 years?* (\$11,273.28) \#3 *If you invested \$2,000 for 60 months at 4.5% compounded semi-annually, how much money would you have in the account at the end of 60 months?* (\$2,498.41) *How much of this is interest?* (\$114,954.94) \#4 Changing Rates *Suppose you placed \$10,000 in an investment. Find the maturity value after five years for 8% compounded semi-annually for two years followed by 6% compounded annually.* (\$13,933.20) 9.3 PRESENT VALUE \#1 *How much will you need to invest today to have \$14,000 in 14 years at 9% compounded semi-annually?* (\$4,081.99) \#2 *How much will you need to invest today to have \$200,000 in 11 years at 7.85% compounded quarterly?* (\$85,045.06) *How much of this is interest?* (\$114,954.94) \#3 *A debt of \$37,000 is owed 21 months from today. If prevailing interest rates are 6.55% compounded quarterly, what amount should the creditor be willing to accept today?* (\$33,023.56) \#4 *Tom's property taxes of \$5450 are due on July 1. What amount should the city accept if the taxes are paid eight months in advance and the city can earn 3.6% monthly on surplus funds?* \#5 Equivalent Payment *Amadala owes Nik \$3,000 and \$4,000, due nine months and two years from today, respectively. If she wants to pay off both debts today, what amount should she pay if money can earn 6% compounded quarterly?* (\$6419.80) 10.1 CALCULATING THE INTEREST RATE \#1 *If your investment of \$5,000 grew to \$12,175.94 after 10 years, what quarterly compounded nominal interest rate did you earn?* (9.0%) \#2 *If you invested \$2,000 for 60 months which grew to a maturity value of \$2498.41,* *what nominal rate of interest compounded semi-annually did the investment earn?* (4.5%) *\#3 Five years ago, Taryn placed \$15,000 into an RRSP that earned \$6,799.42 of interest compounded monthly. What was the nominal interest rate for the investment?* (7.5%) *Note: FV = PV + Interest earned = 15,000 + 6,799.42 = 21,799.42* \#4 *At what monthly compounded interest rate does it take five years for an investment to double?* (13.94%) *Note: PV can be any amount as long as FV is double it*