Beverly Hills started a paper route on January 1, 2009. Every three months, she
ID: 2645134 • Letter: B
Question
Beverly Hills started a paper route on January 1, 2009. Every three months, she deposits $650 in her bank account, which earns 8 percent annually but is compounded quarterly. On December 31, 2012, she used the entire balance in her bank account to invest in an investment at 7 percent annually.
How much will she have on December 31, 2015? Use Appendix A and Appendix C for an approximate answer, but calculate your final answer using the formula and financial calculator methods. (Do not round intermediate calculations. Round your final answer to 2 decimal places.
How much will she have on December 31, 2015? Use Appendix A and Appendix C for an approximate answer, but calculate your final answer using the formula and financial calculator methods. (Do not round intermediate calculations. Round your final answer to 2 decimal places.
Explanation / Answer
Step1: Computation of Future value of Annuity for the period January 1, 2009 to December 31 , 2012.We have,
Futrue Value of Annuity = A [ (1 + r)n - 1] / r
Where,
A = Deposit Amount = $ 650
r = rate of interest( Compounded quaterly) = 8/4 = 2.00 % Compouded quaterly
n = time period = 3 x 4 = 12 periods
Putting the value in above formula,We have,
Futrue Value of Annuity = 650 [ (1.02)12 -1] / 0.02 = 650 [ 1.2682 -1] / 0.02 = 650[13.41] = $ 8,718
Hence, Total amount of Beverly Hills as on December 31,2012 is $ 8,718.
Step2: Computation of total amount as on December 31,2015 when she invest all amount @ 7%.We have,
Future value of investment = A(1+r)n
Future value of investment = 8,718 ( 1+0.07)3 = 8718 (1.07)3 = 8,718 x 1.225 = $ 10,679.55
Hence, total amount received by her as on date December 31,2015 is $ 10,679.55
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