In exercises 37,38 & 50, we consider the effects of starting early or late to sa
ID: 3196351 • Letter: I
Question
In exercises 37,38 & 50, we consider the effects of starting early or late to save for retirement. Assume that each account considered has an APR of 6% compounded monthly.
37) At age 20, you realize that even a modest start on savings for retirement is important. you begin depositing $50 each month into an account. what will be the value of your nest egg when you retire at age 65?
38) Against expert advice, you begin your retirement program at age 40. You plan to retire at age 65. what monthly contribution do you need to make to match the nest egg from exercise 37?
40) Let's return to the situation in Exercise 37: At age 20, you begin depositing $50 each month into an account. Now suppose that at age 40, you finally get a job where your employer puts $400 per month into an account. you continue your $50 deposits, so from age 40 on, you have two separate accounts working for you. what will be the total value of your nest egg when you retire at age 65?
Explanation / Answer
Question 37%
As here we are given the APR = 6% compunded monthly.
the nest egg when retire at 65 =
Here if we take interest rate of 6% percent this amount will be, let say FV
Period = 12 * 45 = 540
Rate = 6/100 = 0.06 annual
FV = P * [(1 + r/12)t -1]/r = 50 * [{ (1 + 6/1200)540 -1] /(0.06/12)= $ 1,37,800
Question 38
Here lets say we are putting x amount from age 40.
here number of periods = (65 - 40) * 12 = 300
so as we have to equal the amount of the nest egg started from age 20.
that means
X [(1 + 0.005)300 -1] /(0.06/12) = 137800
X = $ 198.85
Question 40
Here nest egg of $ 50 amount = $ 137800
Nest egg of $ 400 amount for 25 years = 400 * [{ (1 + 6/1200)300 -1] /(0.06/12) = 277197.58
Total nest egg at retirement = $ 137800 + $ 277197.58 = $ 441998