Project 3 YOUR NAME____________________________________________ This project contains questions from Chapter 10 project page 522 Exercises Solutions Hints 1. Suppose a $100,000 investment grows 3% during the first year and 4% during the second year. By what percent will it have grown after the two-year period? Find the interest earned after the 1st year ANS_____________________ Find the interest earned in the 2nd year (on current balance) Investment grows from pres by adding an interest amoun current balance I = B*i*n Current balance is the future ANS_____________________ Find the interest earned after the two years ANS_____________________ Find the interest rate at which the original investment would earn the interest after the 2nd year. ANS_____________________ 2. Rework Exercise 1 for the case where the investment earns 4% during the first year and 3% during the second year. Is the answer to Ex 2 greater, less than, or equal to the answer to Ex 1. (show calculation here) ANS______________________________________ 3. Consider an annuity in which $100000 is invested and $10000 is withdrawn at the end of each year. Suppose the interest rate is 3% during the first year and 4% during the second year. What is the balance at the end of the second year? Find the interest after the first year ANS__________________ Work out year 1 first. Find th Work out year 2. Use still formulas of Ex 1 F= Find the current balance after year 1 ANS__________________ Find the interest earned in the second year ANS__________________________ Find the balance after the second year ANS__________________________ 4.Rework Ex3 where the interest rate is 4% during the first year and 3% during the second year. Is the balance at the end of the second year greater than, less than, or equal to the answer to Ex 3? (show calculation here) ANS______________________________________________ 5.(this is Exercise 8 page 522) Which of the following statements is true? a) Suppose an investment of P dollars earns 4% one year and loses 4% the next year Then the value of the investment at the end of the two-year period will be P dollars. Find interest after year1 Work out year one and year When investment loses valu Use any value for P ANS__________________ Find current balance after year one ANS___________________ Find interest after year two ANS____________________ Find current balance or value of the investment after year two ANS_______________________ ANS_____________________TRUE OR FALSE b) Suppose investment A earns 4% one year and then loses 3% the next year, and investment B loses 3% one year and then gains 4% the next year. Then the balances of the two investments will be the same after the two-year period. for investments A B Find interest after year1 Use $1000 for the principal ANS__________________ Find current balance after year one ANS___________________ Find interest after year two ANS____________________ Find current balance or value of the investment after year two ANS_______________________ ANS_____________________TRUE OR FALSE 6. (Exercise 9 page 522) Show that if $1000 is invested at 8% compounded annually, then it will double in about 9 years. (Note: 9= 72/8, the rule of 72) years F 1 2 3 4 5 6 7 8 9 10 11 Calculate and determine in the investment is doubled. 7. (Exercise 10) Show that if $1000 is invested for 6 years, then it will approximately double in that time if it appreciates at 12% per year compounded annually.( Note 12=72/6) interest rate F 1 2 3 Calculate and determine at the investment is doubled. 4 5 6 7 8 9 10 11 12 13 14 Investment grows from present value P to a future value F = P + I by adding an interest amount I. Interest amount is earned on the current balance I = B*i*n Current balance is the future value. Work out year 1 first. Find the current balance for the year 2. Work out year 2. Use still formulas of Ex 1 F=P+I and I=B*i*n Work out year one and year two. When investment loses value F=P-I. Use any value for P Use $1000 for the principal of both investments. Calculate and determine in which year the investment is doubled. Calculate and determine at which interest rate the investment is doubled. 7. (Exercise 10) Show that if $1000 is invested for 6 years, then it will approximately double in that time if it appreciates at 12% per year compounded annually.( Note 12:72/6) interest rate F 1 Calculate and determine at which interest rate 2 the investment is doubled. 3 4 5 6 7 8 9 10 11 12 13 14 7. (Exercise 10) Show that if $1000 is invested for 6 years,.3 then it will approximately double in that .3 time .3 if it appreciates at 12% per year compounded annually.( Note 12:72/6) 3 J F = (1 + i)"P3 P = $1000 and i = 12%. Year .3 F = (1 + i)"P.3 .3 1.3 $1 ,1203 .3 2.3 $1 254.43 .3 3.3 $1 ,404.93.3 .3 4.3 $1,573.52 .3 5.3 $1 ,762.34.3 .3 6.3 $1,973.82 .3 7.3 $2,210.683 .3 8.3 $2,475.963 .3 9.3 $2,773.083 .3 10.3 $3,105.84 .3 11.3 $2,331 .64.3 .3 b) Suppose investment A earns 4% one year and then loses 3% the next year, and investment B loses 3% one year and then gains 4% the next year. Then the balances of the two investments will be the same after the two-year period. for investments From the formula, we know that the order of the two number I and s does not affect the balance Thus, it is true that the two investment will be the same after the two year period= so the answer is that lstatemerlt (b)| is true Find interest after year1 ANS Find current balance after year one ANS Find interest after year two ANS Find current balance or value of the investment after year two ANS AME TPl IF b) Suppose investment A earns 4% one year and then loses 3% the next ,, year,' ,, and investment B loses 3% one year and then gains 4% the next year": , , Then the balances of the two investments will be the same after the two-year period\": .1 Investment A earns 4% one year and loses 3% the next year, so the value of the variable LA 2 4 and s3, = -3, investment B loses 3% one year and gain 4% the next year, so the value of the variable are 1:3 = -3 and g = 4 4 From the formula, we know that the order of the two number r and s does not affect the balance Thus, it is true that the two investment will be the same after the two 7 year period, so the answer is that |statement (b)| is true L 3) Suppose an investment of P dollars earns 4% one year and loses 4% the next year Then the value of the investment at the end of the two-year period will be P dollars. If an investment of $P earns r% one year and 5% the following year, then the balance after the two year period is P(1 + r/100)(1 + s/ 100) a) If an investment of P dollars earns 4% one year and loses 4% the next year, then the balance at the end of the two 7 year period is given by the previous formula with r = 4% and [Balance after two year] = P[l + 4/100]*[174/100] : P(l .04)(0.96) : 0.99S4P Thus, it is false that the value of the investment will he $P a) Suppose an investment of P dollars earns 4% one year and loses 4% the next year Then the value of the investment at the end of the two-year period will be P dollars. If an investment of $P earns r% one year and 5% the following year, then the balance after the two year period is P(1 + r/100)(1 + s/ 100) a) If an investment of P dollars earns 4% one year and loses 4% the next year, then the balance at the end of the two 7 year period is given by the previous formula wit [Balance after two year] = P[1+ 4/100]*[17 4/100] : P(1.04)(0.96) : 0.9984P Thus, it is false that the value of the investment will be $P Find interest after year1 I 1 Work out year one and year two. When investment loses value F=P-l. Use any value for P ANS Find current balance after year one ANS Find interest after year two ANS 3) Suppose an investment of P dollars earns 4% one year and loses 4% the next year Then the value of the investment at the end of the two-year period will be P dollars. If an investment of $P earns r% one year and 5% the following year, then the balance after the two year period is P(1 + r/100)(1 + s/ 100) a) If an investment of P dollars earns 4% one year and loses 4% the next year, then the balance at the end of the two 7 year period is given by the previous formula with r = 4% and [Balance after two year] = P[l + 4/100]*[174/100] : P(l .04)(0.96) : 0.99S4P Thus, it is false that the value of the investment will he $P a) Suppose an investment of P dollars earns 4% one year and loses 4% the next year Then the value of the investment at the end of the two-year period will be P dollars. If an investment of $P earns r% one year and 5% the following year, then the balance after the two year period is P(1 + r/100)(1 + s/ 100) a) If an investment of P dollars earns 4% one year and loses 4% the next year, then the balance at the end of the two 7 year period is given by the previous formula wit [Balance after two year] = P[1+ 4/100]*[17 4/100] : P(1.04)(0.96) : 0.9984P Thus, it is false that the value of the investment will be $P Find interest after year1 I 1 Work out year one and year two. When investment loses value F=P-l. Use any value for P ANS Find current balance after year one ANS Find interest after year two ANS