| | Issues |
| | Issue A: | | | | | Issue A |
| | For the last 19 years, Mary has been depositing $500 in her savings account , which has earned 5% per year, compounded annually and is expected to continue paying that amount. Mary will make one more $500 deposit one year from today. If Mary closes the account right after she makes the last deposit, how much will this account be worth at that time? | | | | | From Appendix C:
FVA = A × FVIFA (5%, 20 periods)
FVA = $500 × xx.xxx = $xxxxx.00
|
| | Issue B: | | | | | Issue B: |
| | Mary has been working at the university for 25 years, with an excellent record of service. As a result, the board wants to reward her with a bonus to her retirement package. They are offering her $75,000 a year for 20 years, starting one year from her retirement date and each year for 19 years after that date. Mary would prefer a one-time payment the day after she retires. What would this amount be if the appropriate interest rate is 7%? | | | | | From Appendix D: PVA = A × PVIFA (?%, ? periods)
PVA = $75,000 × xx.xxx = $xxxxxx
|
| | Issue C | | | | | Issue C: |
| | Mary’s replacement is unexpectedly hired away by another school, and Mary is asked to stay in her position for another three years. The board assumes the bonus should stay the same, but Mary knows the present value of her bonus will change. What would be the present value of her deferred annuity at 7%? | | | | | Deferred annuity—From Appendix D PVA = A × PVIFA (i = ?%, ? periods)
PVA = $xx,000 × 10.594 = $794,550
Now, discount back this value for three periods
PV = FV × PVIF (i = 7%, 3 periods) Appendix B
PV = $794,550 × 0.xxx = $xxxxxx.xx
|
| | Issue D |
| | Mary wants to help pay for Beth’s education(her granddaughter). She has decided to pay for half of the tuition costs, which are now $11,000 per year at State University. Tuition is expected to increase at a rate of 7% per year into the foreseeable future and Beth just had her 12th birthday. Beth plans to start college on her 18th birthday and finish in four years. Mary will make a deposit today and continue making deposits each year until Beth starts college, and will earn 4% compounded annually on this account. How much must Mary’s deposit be each year in order to pay half of Beth’s tuition at the beginning of each school each year? |
| | Solution |
| | Step 1: Calculate the tuition amounts at the time the tuition will be paid. |
| | T1 = $11,000(FVIF7%,6) = $16508 |
| | T2 = $11,000(FVIF7%,7) = $ |
| | T3 = $11,000(FVIF7%,8) = $ |
| | T4 = $11,000(FVIF7%,9) = $ |
| | Step 2: Calculate Mary’s Contribution to the tuition pool: |
| | T1 = $11,000(FVIF7%,6) = $xxxxx = $xxxx |
| | T2 = $11,000(FVIF7%,7) = $ = $ |
| | T3 = $11,000(FVIF7%,8) = $ = $ |
| | T4 = $11,000(FVIF7%,9) = $ = $ |
| | Step 3: Find the amount that needs to be in the bank at the time Beth starts college: |
| | T1 = $11,000(FVIF7%,6) = $xxxxx = $xxxx = $xxxx |
| | T2 = $11,000(FVIF7%,7) = $1x = $x = x(PVIF4%,1) = $ x |
| | T3 = $11,000(FVIF7%,8) = $18900 = $9450 = x(PVIF4%,2) = $x |
| | T4 = $11,000(FVIF7%,9) = $20224 = $10112 = 10112(PVIF4%,3) = $xxxx |
| | xx,xxx |
| | Step 4: Find the payment required to accumulate Beth share of the tuition: |
| | $34,460 = PMT(FVIFA 4%, 7) |
| | PMT = $xxxx.xx |
cabo1789
week_3_lasa_help.xlsx
