Question

1. You expect a solid job offer after you graduate from Mercer’s accounting program. You plan to deposit $500 per month into an individual retirement account (IRA) in Bank of America’s Decatur branch. The deposit will be automatically deducted from your monthly paycheck from E&Y Atlanta at the end of each month starting June 30, 2020. The IRA is paying 8% per year compounded monthly. What is the value of your account at the end of the 10-year period?

2. You plan to purchase a small office near the five-corners in downtown Atlanta for $50,000 at the end of year 2019. You estimate that by renting out that office space, you will receive a stream of rental income for the coming eight years at the end of each year as shown in below. After eight years, you estimate that you can still sell the office space for $45,000 (hopefully) at the end of the eighth year. Is this project a good investment if you project that the normal rate of return in this line of business is 12%? How about if the general rate of return is 15%? 8%? Year 1 $6,000 Year 2 $6,500 Year 3 $7,000 Year 4 $7,500 Year 5 $7,500 Year 6 $8,500 Year 7 $8,500 Year 8 $8,500

3. Based on the information provided in Step 2 above, compute the Internal Rate of Return for the investment.

4. While you are bored by the recent lockdown, you have decided to drive out to spent several dollars to buy a Georgia Educational Lotto and were lucky enough to win a $1 million prize. The prize is to be awarded in 20 annual payments of $50,000 each, payable directly to your Bank of America account in Duluth at the end of the year each year. When the news of your winning was out, a person from Cash-Today-Enjoy-Now approached you immediately to offer you the option of receiving a lump sum payment of $400,000 right away, which, from your research, you know you can invest in an IRA account that pays 12% compounded annually for the coming 20 years. a. What is the present value of the $50,000 annuity? Use the projected 12% rate as the rate that the alternative IRA account will pay. b. What should your decision be per the prize you win in lotto? Why?

5. Your Uncle recently gave you $10,000 gift to celebrate your college graduation. You immediately invested that $10,000 into the Brighter Atlanta Bond that matures in five years with a value of $18,000 at maturity. If the bond interest is compounded monthly, what is the monthly interest rate for this investment?

6. You have decided to deposit some money each year into your bank account for future investments. Since you were from New England area originally, you would like to accumulate $100,000 as your down payment for a house in suburban Boston so that you could enjoy the fun of snow plowing (ah, skiing) in winter. If you deposit $2,000 per year into an account that earns 10% interest per year compounded annually, how long does it take for you to accumulate the $100,000 target? If you would like to shorten the number of years to five years with the same 10% return annually, how much do you need to deposit per year at the end of each year?

Answer 1

First Question
Deposit monthly	500
Rate of interest per year	8%
Monthly compunded rate of return =(((1.08)^(1/12))-1))*100	0.643403
Time period in months	120
Future value	1079.462
Second Question
Initial investment	50000
Terminal value	45000
Rate of return	12%
Particulars	1	2	3	4	5	6	7	8	8th year included (Cash flow and terminal value=8500+45000)
Cash flows	6000	6500	7000	7500	7500	8500	8500	53500
Discount factor	1.12	1.2544	1.404928	1.573519	1.762342	1.973823	2.210681	2.475963176
Present value	5357.143	5181.76	4982.462	4766.386	4255.701	4306.365	3844.968	21607.7527
Sum of present value	54302.54
NPV	4302.537
As NPV is positive it is a good investment
Part A if rate of return is 15%	15%
Particulars	1	2	3	4	5	6	7	8	8th year included (Cash flow and terminal value=8500+45000)
Cash flows	6000	6500	7000	7500	7500	8500	8500	53500
Discount factor (1+r)^n	1.15	1.3225	1.520875	1.749006	2.011357	2.313061	2.66002	3.059022863
Present value	5217.391	4914.934	4602.614	4288.149	3728.826	3674.785	3195.465	17489.2449
Sum of present Value	47111.41
NPV	-2888.59
As NPV is negative it is a profitable business
Part B if rate of return is 8%	8%
Particulars	1	2	3	4	5	6	7	8	8th year included (Cash flow and terminal value=8500+45000)
Cash flows	6000	6500	7000	7500	7500	8500	8500	53500
Discount factor (1+r)^n	1.08	1.1664	1.259712	1.360489	1.469328	1.586874	1.713824	1.85093021
Present value	5555.556	5572.702	5556.826	5512.724	5104.374	5356.442	4959.668	28904.38532
Sum of present value	66522.68
NPV	16522.68
As NPV is positive it is a good investment
Third Question
Internal rate of return	13.7215%
Particulars	1	2	3	4	5	6	7	8	8th year included (Cash flow and terminal value=8500+45000)
Cash flows	6000	6500	7000	7500	7500	8500	8500	53500
Discount factor (1+r)^n	1.137215	1.293258	1.470712	1.672516	1.90201	2.162995	2.45979	2.797310243
Present value	5276.047	5026.066	4759.598	4484.262	3943.196	3929.737	3455.579	19125.51535
Sum of present value	50000
IRR is that rate for which NPv is 0	13.7215%
Fourth Question
Annual payments	50000
Time period	20
Rate of return	12%
Present value
Particulars	1	2	3	4	5	6	7	8	9	10	11	12
Payment	50000	50000	50000	50000	50000	50000	50000	50000	50000	50000	50000	50000
Discount factor (1+r)^n	1.12	1.2544	1.404928	1.573519	1.762342	1.973823	2.210681	2.475963176	2.773079	3.105848	3.47855	3.895976
Present value	44642.86	39859.69	35589.01	31775.9	28371.34	25331.56	22617.46	20194.1614	18030.5	16098.66	14373.81	12833.75
Sum of Present value	309718.7
As the present value which is 309718.7 is less than 400000 I should take the lump sum payment right away as there 400000 invested now at 12% will yield higher than the lottery prize money
Fifth question
Present value	10000
Final value	18000
rate of return in months	r
time period in months	60
So 18000=10000(1+r)^60
(1+r)^60	1.8
1+r	1.009845
r=	0.009845
r (in %)	0.984459
Sixth question
Part A
Payment deposited annually C	2000
Rate of interest	10%
Final value	100000				20000	100000	5	6
Future value of annuity is given by ((C/r)*(((1+r)^n)-1))=100000								1.791759469	0.09531
								18.7992455
So n	18.8
It will take 18 years and 8 months to accumulate 100000
Part B
C	?
r	10%
n	5
Final value	100000
Applying the same concept of annuity and formula as shown above						1.61051	0.61051	6.1051	16379.75
(1+r)^n	1.61051
X=((1+r)^n)-1	0.61051
X/r	6.1051
C	16379.75