VIEWS: 18 PAGES: 3 POSTED ON: 9/16/2012
Name:____________________________Date:____________Period:___ Exponential Applications -Finance (Notes) There are two important functions that financial institutions use to calculate the balance of their clients’ F rI A P 1 nt accounts. The first of these is: o H nK where A is the amount when Po dollars is deposited at an interest rate of r compounded n times per year for t years. Example 1 Example 2 How much does a person have in their account How much does a person need to deposit in their after 5 years if they deposited $2000 at an account so that after 6 years they have $5000 if interest rate of 2.3% compounded monthly? the account pays an interest rate of 4% compounded daily? Po=2000, t=5, r=0.023, n=12 (monthly). Find A. A=5000, t=6, r=0.04, n=365 (daily) Find Po. F .023I A 2000 1 ( 12 )( 5 ) H 12 K F .04 I 5000 P 1. ( 365 )( 6 ) A 2000a .00192f 1 ( 60 ) H 365K o 5000 P a .0010959f 1 ( 2190 ) A 2000a 100192f ( 60 ) o . 5000 P a 10010959f ( 2190 ) . A 2000(112175) . o A 224350 . 5000 Po (127123) . 1 1 5000 Po (127123) . . 127123 . 127123 393319 Po . The second common function is the one financial institutions use to compound interest continuously. It rt is: A Pe Example 3 Example 4 How much does a person have in their account How much will a person need to deposit in their after 5 years if they deposited $2000 at an account so that after 6 years they have $5000 if interest rate of 2.3% compounded continuously? the account pays an interest rate of 4% P=2000, t=5, r=0.023, Find A. compounded continuously? A=5000, t=6, r=0.04, Find Po. A 2000e 0.023( 5) 5000 Pe.24 A 2000e.115 5000 P(127125) . A 2000(112187) . 1 1 A 2243.75 5000 P(127125) . . 127125 . 127125 393314 P . SATEC/Algebra II/Exponential Functions/6b525301-4602-4ed3-843b-bf4b90150343.doc/Rev. 07-01 Page 1/3 A businesswoman wishes to invest $25,000 at 6% interest at your bank which compounds interest monthly. She wants to know how many years it will take to double her money at this interest rate. The function for the amount in an account after “t” years is: F r I A(t ) PG J where nt H nK 1 A(t) is the amount in the account after t years P is the principal invested r is the interest rate expressed as a decimal n is the number of compounding periods in a year Find the length of time in years it will take for the account to reach $50,000. (Hint: use logarithms and their properties to solve.) SHOW ALL WORK! The NCAA holds a championship basketball tournament each spring. The nation’s top 64 teams in Division 1 are invited to play. When a team loses, it is out of the tournament. Determine the number of teams left in the tournament after round 5. Write an equation in the form y=abx to solve this. (Hint: a is the initial number of teams, and b is the rate at which they are being eliminated.) Be sure to show all work. A biologist is observing a strain of bacteria growing in a petri dish. The population of the bacteria increases exponentially over time. If the 1st bacteria took 1 hour to divide into 2 bacteria, how long will it take for 30 bacteria in the disk to grow to at least 1000? Make sure your write down your equation and show all work. SATEC/Algebra II/Exponential Functions/6b525301-4602-4ed3-843b-bf4b90150343.doc/Rev. 07-01 Page 2/3 Exponential Applications -Finance Answer the following, showing all your work on a separate piece of paper. 1. Jackie is buying a house. The amount 5. Elsa has her eye on a $14,450 car. of their loan for the house is She plans to take out a loan for the $108,000. The loan Jackie will take car. The Dealer offers her 8.4% out charges 5.55% annual interest. If interest rate compounded monthly. the loan is for 15 years, how much will How much will she save if she takes the monthly payments be? out a 4-year loan as opposed to a 5- year loan? 2. Maria Gonzalez needed to decide into which bank to deposit her $3000 6. Which would be the better deal for savings. Bank One offered her 4.7% Lonnie a loan for $2500 at 2.5% interest compounded daily but she had interest compounded annually for four to keep her money in the bank for at years, or a loan for $2500 at 3.5% least 4 years. Frost Bank offered interest compounded continuously for 4.8% interest compounded three years? Explain your reasoning. semiannually with the same condition that she had to keep her money in the 7. Karen has $5000 to invest in two bank for at least 4 years. Which bank stocks. She decides to invest $3200 should she go with and why? in LIQD stock that pays 11.3% interest and $1800 in DISNEY stock 3. John Matterson wishes to save $7000 that pays 10.5% compounded daily. as a down payment for a car that he How much money would she make plans to buy in 6 years. How much after investing for two years? money should he deposit into a Money Market account that pays 6.5% 8. Estimate the time it will take for an interest compounded continuously to investment of $2500 to double in earn his down payment? value if it is invested at 8% interest. 4. Jason and Lucia are buying a house. 9. Estimate the time it will take for an The amount of their loan for the investment of $2500 to triple in value house is $98,000. They secured a if it is invested at 8% interest. loan, which charges 6.75% annual interest. If the loan is for 30years, how much will the monthly payments be? SATEC/Algebra II/Exponential Functions/6b525301-4602-4ed3-843b-bf4b90150343.doc/Rev. 07-01 Page 3/3