Question

answer both please

12. Now let's work backwards. Assume that you will all live until 100 (a good news!), but will have to retire by 65 (a bad news^^). You estimate that you will need to draw at least $3,000 per month of living expenses out of your retirement account after you retire (assume no inflation). Suppose that your retirement account will keep earning 6% APR after you retire. If you want to ensure that your retirement account will not run out of money before the age of 100, how much should you have in your retirement account when you retire at 65?

13. Given your answer to Question 12 and your current age, how much should you save and put into the retirement account per month to achieve the goal at 65? Assume that you can earn 6% APR with monthly compounding on your investments.

Answer 1

12. Assume that you will all live until 100 and you will have to retire by 65; therefore you have 100-65 =35 years after retirement

You estimate that you will need to draw at least $3,000 per month of living expenses out of your retirement account after you retire

After retirement you will be able to earn 6% APR

Therefore you have to calculate Present value of the total monthly withdrawals of $3,000 for 35 years at the time of retirement with the help of PV of an Annuity formula

PV = PMT * [1-(1+i) ^-n)]/i

Where,

Present value at the time of retirement (PV) =?

PMT = Monthly payment = $3,000

n = N = number of payments = 12 *35 years = 420

i = I/Y = interest rate per year =6%; therefore monthly interest rate = 6%/12 = 0.5% per month

Therefore,

PV = $3,000* [1- (1+0.5%) ^-420]/0.5%

= $526,140.68

You should have$526,140.68 in your retirement account when you retire at 65.

13. Given your answer to Question 12 and your current age, how much should you save and put into the retirement account per month to achieve the goal at 65? Assume that you can earn 6% APR with monthly compounding on your investments.

Your retirement account will have $526,140.68

Now this amount will be future value of all your savings

Assume that you are 25 years old; therefore time for retirement = 65 years – 25 years = 40 years (You can assume a different number also but method of calculation will be same)

We can use FV of an Annuity formula to calculate the monthly savings by you

FV = PMT *{(1+i) ^n−1} / i

Where,

Future value of annual savings FV = $526,140.68

PMT = Monthly savings =?

n = N = number of payments = 12 *40 years = 480

i = I/Y = interest rate per year =6%; therefore monthly interest rate = 6%/12 = 0.5% per month

Therefore,

$526,140.68 = monthly savings *{(1+0.5%) ^480−1} /0.5%

Monthly savings = $264.19

Therefore you have to save $264.19 per month to achieve your retirement goal at age of 65.