Question

Beverly Hills started a paper route on January 1. Every three months, she deposits $1,000 in her bank account, which earns 8 percent annually but is compounded quarterly. Four years later, she used the entire balance in her bank account to invest in an investment at 12 percent annually. How much will she have after three more years? 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.)

Future value:

Answer 1

In the first half of the question, 1 Period = 3 Months.

Periodic Payments (A) = $1000

Rate = 8% annually (compounded quarterly). Therefore, Rate per Period (r) = 8% / 4 = 2%

Number of Periods (n) = 4 years x 4 = 16 periods

Using Appendix C,

FV_A = A x FVIFA ( 2% , 16 periods)

FV_A = 1000 x 18.639 = $18639

Using Formula,

FV_{A =} $18639.29

Using Calculator,

Enter N = 16, I/Y = 2, PV = 0, PMT = 1000

Press CPT, then FV.

FV = $18639.29

This is the Value she will have in her bank account after 4 years. After this, she invests the entire amount for 3 years @ 12 percent annually.

Using Appendix A,

FV = PV x FVIF ( 12%, 3 Periods)

FV = 18639 x 1.405 = $26,187.80

Using Formula,

FV = PV x (1 + r)ⁿ

FV = 18639.29 (1.12)³ = $26186.86

Using Financial Calculator,

Enter N = 3, I/Y = 12, PV = 18639.29, PMT = 0

Press CPT and then FV.

FV = 26186.86