Question

1) Ishan and Hazel plan to retire at age 60 with a retirement income of $48,000 a year from their savings. Rather than pay themselves the whole amount at the beginning of each year, they have decided that payment at the beginning of each quarter of $12,000 gives them the right balance of flexibility and maximized interest earnings. They feel they can safely earn an interest rate of 8%, compounded quarterly, on their money and they are budgeting based on the prediction that they will live until they are 90 years old.    How much money will they have to have saved by the time they are 60 in order to reach their retirement goal?

2) Now that Ishan and Hazel have their saving goal calculated they want to start budgeting to reach that goal. They are 40 years old, so they have just 20 years to save up the total they calculated they would require so that they can still reach their goal of retirement by age 60. If they assume the same interest rate, and make deposits into their savings at the beginning of every month, how much would their deposit have to be each month?  

Answer 1

SOLUTION

IN this given question there are two partners i) Ishan and, ii) Hazel and they want to retire at the age of 60 years with the retirement income of $48000 a year from their savings.

They have decided that payment is to be made at the beginning of each quarter of $12000 and the interest rate is 8% compounded Quarterly

We have to find out How much money will they have to have saved by the time they are 60 in order to reach their retirement goal?

In this question, we have to find out the present value of annuity

Present value of an annuity with the beginning of the time period payments

PV= [(a*(1-1/(1+r)^n))/r)*(1+r)

Here PV = Present value of annuity

a= Annuity

n= Number of time period

r= rate of interest

Here a= $12000

n= 90-60 years i.e 30 years and we have converted it into quarters form i.e. 30 years * 4 = 120 quarters

r= 1/100 i.e .01

so putting the value

PV =[12000*(1-1/(1+.01)^120))/.01)*(1+.01)]

we get PV = $844770.327

so   they have to have saved $844770.327 by the time they are 60 in order to reach their retirement goal.