Question

You are saving for retirement. To live​ comfortably, you decide you will need to save $ 4 million by the time you are 65. Today is your 25 th ​birthday, and you​ decide, starting today and continuing on every birthday up to and including your 65 th ​birthday, that you will put the same amount into a savings account. If the interest rate is 3 %​, how much must you set aside each year to make sure that you will have $ 4 million in the account on your 65 th ​birthday?

Answer 1

Answer: $50,846.3701

Step-by-step explanation:

Need to save $4 million to live comfortably,

Interest rate, r = 3%

N = 40 years

`Present\ value=(FV_(N) )/((1+i)^(N))`

`Present\ value=(4,000,000 )/((1+0.03)^(40))`

`Present\ value=(4,000,000 )/(3.262)`

= 1,226,241.57

`Present\ value\ of\ annuity= C*(1)/(i)*(1-(1)/((1+i)^(N))) + C`

`1,226,241.57= C*(1)/(0.03)*(1-(1)/((1.03)^(40)))+C`

`1,226,241.57= C*(1)/(0.03)*(1-(1)/((1.03)^(40)))+C`

`1,226,241.57=C[(1)/(0.03)*(1-0.3065)+1]`

`1,226,241.57=24.1166* C`

`C=(1,226,241.57)/(24.1166)`

= $50,846.3701

Hence, $50,846.3701 will be the annual payment to have $4 million in the account on 65th birthday.