Question

Today is Derek’s 25th birthday. Derek has been advised that he needs to have $2,041,270.00 in his retirement account the day he turns 65. He estimates his retirement account will pay 6.00% interest. Assume he chooses not to deposit anything today. Rather he chooses to make annual deposits into the retirement account starting on his 30.00th birthday and ending on his 65th birthday. How much must those deposits be?

If Derek plans to deposit $11,833.00 into his retirement account on each birthday beginning with his 26th and the account earns 8.00%, how long will it take him to accumulate $3,187,255.00?

Answer 1

Number of years of deposit = 36

Let the annual deposit be X

X*[{(1.06)^36-1}/0.06] = 2,041,270

119.12x = 2,041,270

X =$17,136.25

Deposit amount should be =$17,136.25

Let it takes X years

11,833*[{(1.08)^X -1}/0.08] = 3,187,255

(1.08)^x - 1 = 21.55

X = 41(approx.)

Hence, it will take 41 years to accumulate this amount

I.e. till his 66th bday