Retirement Savings Calculation and Investment Analysis

This finance homework assignment analyzes a retirement plan for Michelle, who is currently 25 years old and plans to retire at 62. The assignment involves calculating the monthly savings needed to fund a 28-year annuity that will provide $3000 per month starting at age 62. The solution explores two investment options: a portfolio of technology stocks and mutual funds, calculating future values for each investment over 37 years. The assignment utilizes financial formulas, including future value and present value of annuity due, to determine the required monthly savings amount. References from Altınkılıç, Hansen & Ye (2016) and Clare, A., Sherman & Thomas (2016) are included to support the analysis. The final calculation reveals that Michelle needs to save $316.46 each month to achieve her retirement goals.

MATH
MATH

MATH
Answer
Michelle who is now 25years old and she will retire at when she will turn 62. After retirement
she wants to invest in 28years annuity plan which will give a return of $3000 per month. The
return of $3000 per month on the investment should start when she will turn 62. The 28 years
annuity will give return of 3.25% which will be compounded annually. The two options which
she has chosen is 1) investment in portfolio of technology stocks and the other one is 2) mutual
finds. In words of Altınkılıç, Hansen & Ye (2016), portfolio of stock means a group of bonds,
stock, commodities which are held by the financial investors. According to Clare, A., Sherman &
Thomas (2016), mutual funds are a fund in which the investors get a risk free return from his
investment.
Let the monthly savings by Michelle be $X. Michelle wants to put his 50% of $X in option 1 and
50% in option 2.
Option 1 - Portfolio of Technology Stock
Investment (I) = 0.5x per month
Rate of interest (r) = 7.5% per annum (compounded annually)
Term (n) =62-25=37 years
Therefore, Future value (FV) = I [(1+ r) n -1]/r
= 0.5x [1+0.075)37-1]/0.075
=0.5x [(1.075)37-1]/0.075
= 0.5x (14.25-1)/0.075
= 90.17x
Option -2 Mutual Fund
Investment (I) = 0.5X per month
Rate of interest (r) = 4.25% per annum (compounded semi-annually)
Effective Interest Rate (r/k) = 0.0425/2 = 0.02125
Term (n) =62-25=37years

MATH
Effective Term (n/k) = 37*2 = 74
Therefore, Future value (FV) = I [(1+ r/k) n/k -1]/r/k
FV= 0.5x [(1+0.02125)74 -1]/0.02125
= 0.5x [(1.02125)74 -1]/0.02125
=0.5x [4.74-1]/0.02125
= 88x
Now, from the total investment of portfolio and mutual fund i.e. 90.17x + 88x = 178.17x, she
purchased 28years annuity which will give her $3000 per month.
The monthly payment will start from her 62nd birthday; therefore here will apply PV of
ANNUITY DUE formula.
Interest rate (r) = 3.25% p.a. (compounded annually)
Term (n) = 28 years
Monthly return (R) = $ 3000 per month
Therefore, by equating Future value of Total savings with Present value of 28 years annuity we
can get the value of x.
178.17x = (1+r) * R [1-(1+ r)-n]/r
178.17x = (1+0.0325) * 3000 [1-(1+0.0325)-28]/0.0325
178.17x = (1.0325) * 3000 [1-(1+0.0325)-28]/0.0325
178.17x =(1.0325) * 3000 [1-0.4084]/0.0325
178.17x = (1.0325) * 3000 *0.5916/0.0325
178.17x = 1832.4/0.325
X = 316.46
Therefore, Michelle has to save $316.46 each month so that she will receive $ 3000 per month
from her 62nd birthday.

MATH
References
Clare, A., Sherman, M. B., & Thomas, S. (2016). Multi-asset class mutual funds: Can they time
the market? Evidence from the US, UK and Canada. Research in International Business and Finance, 36,
212-221 Avaliabe at http://openaccess.city.ac.uk/17844/1/MULTI%20ASSET%20CLASS%20FUNDS.pdf
[Accessed on 24th march, 2019]
Altınkılıç, O., Hansen, R. S., & Ye, L. (2016). Can analysts pick stocks for the long-run?. Journal
of Financial Economics, 119(2), 371-398. Available at http://www.tulane.edu/~rsweb/Altinkilic,
%20Hansen,%20Ye,%20JFE,%202016.pdf [Accessed on 24th march, 2019]