Assignment 2: LASA 1- The Time of Money
Rodney Schilling
Financial Management
February 26, 2014
Professor Charlie Merritt
Argosy University Online

LASA 1- The Time of Money

In this scenario, I will be giving a detailed report on four different financial issues that Mary has asked me to help her resolve before her retirement. Mary has worked for Argosy University for almost 25 years and is looking to retire in the near future and wants to address several financial issues. Mary has been depositing $500.00 dollars into her savings account every year for the past 19 years and has compounded 5% interest annually and she expected to make one last payment, this time next year. Mary will then close out her account right after that payment and wants to know how much money she will have accrued. For the past 19 years Mary as placed $500.00 dollars into an account making 5% interest compounded annually. Mary will make one last payment into her account; the account will be closed after the last payment has been made. Therefore, I will be looking at how much as $500.00 dollars a year for the past 20 years at 5% interest Mary’s savings has accumulated. I will use future value, because it measures the value of that amount which is allowed to grow at the 5% interest rate over the specified period of time (Block, p.256). This is the formula I will be using:

|FV = Future value |
|PV = Present value |
|i = Interest rate |
|n = Number of periods |

The future value is 5%, I will multiple $500 dollars by 1.050 to get the first year interest earned. The interest earned is $25 dollars so in the first year she has earned $525 dollars; and I know Mary has invested this amount for the past 20 years. Now the formula is FV = PV (1 = i ) ^n; Noe the FV will equal the PV times 1+ 0.5 to the ^n power. this is the 20th power for 20 years of deposits. So we have at 5% for 20 years = 33.066 + $500 dollars for the last payment = $16,533.00

First method (A)
FV = 500 (1=0.05)^20
FV = 500 (33.066) = $ $16,533.00

Second method (B)
PVIFA (7%,20 periods)
PVA - $75,000 x 10.594 = $794,550

The second scenario, Mary has worked for Argosy University for 25 years and has a excellent track record. The university want to reward Mary for her dedication, ethics, professionalism and hard work. The Argosy board of directors wants to reward her for her bonus to her retirement package. Offering her $ 75,000.00 dollars a year for 20 years, starting one year from when Mary is to retire and keep paying her this amount for the next 20 years. Mary is asking for a one time payment the day after she retires; so Mary can invest this amount at the interest rate of 7%. To complete an one time payment it would be 75,000 * 20 years = 1,500,000. To add the 7% we would use the Present Value $1 (Brock,A-9). The 7% column down to the 20 period row = 10.594. using the first initial payment of $ 75,000 dollars and times by the 7% interest rate, this equals $794,550 dollars. Like everything else Mary has a decision to make weather to take payments or accept a one time payment, the choice is hers. Here is the formula that I will be using.
PVA = A x PV IFA (7%, 20 periods)
PVA = $75,000.00 x 10.594 = $ 794,550.00

Third scenario, Now Mary, being an excellent employee for Argosy University, just finds out that she has been asked to work for another three years because her replacement was hired by another school, Boise State University, which has a bad track record for the MBA program (Just saying). Mary has asked me to find out her present value of the bonus she will receive, how it will change and what is the present value if she decides to defer the annuity. To give her an accurate amount I will use her the pervious amount, $ 794,550 dollars and I will subtract the amount by three periods (Brock,A-7). The difference is $146,198 dollars; this is the difference amid the periods.

PVA = A x PVIFA (7%, 20 periods)
PVA = $75,000.00 x 10.594 = $ 794,550.00

Subtracting 3 periods from this value
PV = FV x PVIF (i=7%, 3 periods)
= $ 794,550. x 0.816 = $ 648,589.48

Fourth scenario, Mary being awesome, decides to help her granddaughter pay for half of her tuition at Argosy University. The cost of tuition here is $ 11,000 dollars per year, the tuition is expected to rise to an all time high of 7% per year in the predictable future. Beth just turned 12 years old and being a smart young kid, plans to attend college when she graduates high school at 18. Beth’s goal is to finish college in four years. Mary being wants to make deposits until Beth starts college. This account I set up for them will earn 4% compounded annually. Mary asked me how much she will have to deposit each year until she pays for half of her granddaughter’s college tuition. Well, Beth being 12 years old, will not attend college until she turns 18 years old, this is 6 years from now. The solution is:
IF T1 is the first year’s tuition and so forth,
FV = PV (1 + 7%)^6=$11,000x1.5007 = $16,508
Half the amount = $8,254
T2 = $11,000 (1+7%)^6=$11,000x1.5007 = $17,664
Half the amount = $8,832
T3 = #11,000 (1+7%)^8 = $11,000 x 1.71819 = $18,900
T4 = $11,000 (1+7%)^9 = $11,000 x 1.83846 = $20,223
Half the amount = $10,111.50
At the beginning of beth college the money need to be available at the bank; the money will earn 4% at the bank.
T1 = $8,254
PV = FV/(1+r)^n
T2 = $8,832/(1+4%)^2=$8,492. This amount will grow to $8,832 in one year; that is when the tuition will be due because the bank pays 4% interest.
T3 = $9,450/(+4%)^2 = $8,737
T4 =#10,111.50 (1+4%)^3 = $8,989
I will add T1, T2, T3 and T4 they are all PV terms.

Marry will make a deposit today and for the next six years of college = $34,472 this is the accumulated (FV).
Now Marry will make a deposit today and for the next 7 payments at 4% of interest at the bank.
Annual payments made by Marry = FV of annuity/FV annuity factor = $34,472/[{{(1+4%)^7}/0,04] = $34,472/7.89829
= $4,364 to be deposited now and for the the next six years by Marry.

Reference

Block, S. (2009). Foundations of Financial Management (13th ed). McGraw-Hill Learning Solutions. Retrieved from http://digitalbookshelf.argosy.edu/books/007-737696X/id/ch01