A young engineer wishes to become a millionaire by the time he is 60yrs old. He believes that by careful investment he can obtain a 15% rate of return. he plans to add a uniform sum of money to his investment program each year, beginning on his 20th birthday and continuing through his 59th birthday. How much money must the engineer set aside in this project each year?
This site has a calculator that figures out this problem. Just plug in the numbers.
http://www.moneychimp.com/calculator/compound_interest_calculator.htm
Thank you for the site, I can see it is very useful. I have been able to obtain 4293.33,
but I want to learn how to solve it manually, as during test time I will not be able to use the handy site.
:)
Let P be his annual investment.
You want $1M = P*(1.15)^40 + P*(1.10^39 + ... P(1.15)
= 40P* sum((1.15)^i)
So, with your hand calculator, enter 1.15 -store, *1.15 Mem+ *1.15 Mem+ ...
Take it from here.
To calculate how much money the engineer must set aside each year, we can use the concept of present value. The present value is the current value of a future sum of money, taking into account the time value of money.
In this case, the engineer wants to become a millionaire by the time he is 60 years old. Since he is currently 20 years old, he has 40 years (60 - 20) to save and accumulate wealth.
To find the uniform sum of money he needs to set aside each year, we need to calculate the present value of $1 million at a 15% rate of return over 40 years.
The formula to calculate present value is: PV = FV / (1 + r)^n
Where:
PV = Present Value
FV = Future Value
r = Rate of Return
n = Number of years
Plugging in the values, we have:
PV = $1,000,000 / (1 + 0.15)^40
Calculating this, we find that the present value of $1 million after 40 years at a 15% rate of return is approximately $23,513.29.
So, the engineer must set aside $23,513.29 each year, starting from his 20th birthday and continuing through his 59th birthday, in order to become a millionaire by the time he is 60 years old.