Question

Based on your research, state the lump sum, in $U.S., that you want to have when you retire. This is the future value of your investment; denote it by F. (4 points)

Future value, F $

State the time, in years, that you plan to contribute to your retirement account. Denote this by t. (4 points)

Time, t

Based on the first letter of your last name, choose the annual interest rate for your retirement account from the chart below. It does not necessarily have to be a whole number. Denote this by r, and convert this to its decimal form.

First letter of your last name Possible values for r
A–F 5.00%–6.99%
G–L 7.00%–8.99%
M–R 9.00%–10.99%
S–Z 11.00%–12.99%

Type your chosen value here: (4 points)

Annual interest rate in decimal form, r          

From the table below, choose how many times per year you want to contribute to your retirement fund. Denote this by n, and this will also be your compounding period.
Compounding Period n
Yearly 1
Semi-Annually 2
Quarterly 4
Monthly 12
Weekly 52

Type your chosen value here: (4 points)

Compounding period, n

Calculate the interest rate per compounding period, which you will denote by i, by dividing the annual interest rate from #4 by the compounding period from #5:
i=r/(n )
Round your answer to 6 decimal places.
Interest rate per compounding period, i

Show and explain your work here: (5 points)





Your contribution per period, which you will denote by C, to this retirement account is calculated using the following formula:
C=(F*i)/(((1+i)^((n*t))-1) ).
Using the values that you have chosen for F, i, n, and t, calculate your contribution per period. Use 6 decimal places for your intermediate calculations, and round your final answer to the nearest cent.

Contribution amount, C $




Show and explain your work here: (6 points

Answer 1

I want 1 Million in my retirement fund when I will retire.

Future Value, F = $1,000,000

Currently I am 25 year old and want to retire on 60 year so I have 35 years to retire.

TIme, t = 35 years

My name is Adam Agar (hypothetical).

So first letter of my last name is A

Annual Interest rate, r = 5%

I want to contribute annualy every year in my retirement fund.

Compounding period, n = Yearly, 1

Interest rate per coumpounding period, i = r/(n)

= 5%/1 = 5%

Contribution per period, C = (F*i)/(((1+i)^((n*t))-1))

= (1,000,000 * 5%)/(((1.05)^(35*1) - 1))

= 11,701.707230

Contribution Amount = $11,701.71