a beautiful girl 22 years young has just graduated from college. She accepts a good job and desire to establish her own retirement fund. At the end of each year there after she plans to deposit 2000 in the fund out 15% annual . How old will she when the fund has an accumulated value of 1000000
Ignoring the absurd wording of the question ....
2000(1.15^n - 1)/.15 = 1,000,000
1.15^n - 1 = 75
1.15^n = 76
take logs of both sides and use log rules
n log 1.15 = log 76
n = log 76/log 1.15 = appr 31 years
let me know where you get 15% return in a retirement fund and I will reinvest by pension plan.
Absolutely!! I'd love to find something that gives 15% return!!
To calculate the age at which the retirement fund will have an accumulated value of $1,000,000, we need to determine how many years it will take for the fund to reach that amount.
Step 1: Calculate the annual growth rate
The annual growth rate is 15%.
Step 2: Calculate the amount deposited each year
The girl plans to deposit $2000 at the end of each year.
Step 3: Calculate the time it will take to accumulate $1,000,000
We can use the formula for compound interest to calculate the time it will take to accumulate the desired amount. The formula is:
Final Value = P (1 + r)^n
Where:
Final Value = $1,000,000
P = Annual deposit = $2,000
r = Annual interest rate = 15% = 0.15
n = Number of years
Substituting the given values in the formula, we have:
$1,000,000 = $2,000 (1 + 0.15)^n
Step 4: Solve for n
Divide both sides of the equation by $2,000:
500 = (1 + 0.15)^n
Take the natural logarithm (ln) of both sides:
ln(500) = n * ln(1 + 0.15)
Divide both sides by ln(1 + 0.15):
n = ln(500) / ln(1 + 0.15)
Using a scientific calculator, we can solve:
n ≈ 22.5 years
This means that it will take approximately 22.5 years for the accumulated value of the retirement fund to reach $1,000,000.
Step 5: Calculate the girl's age
Since she just graduated from college at the age of 22, we add the time it takes for the fund to reach the desired value to her age:
22 + 22.5 = 44.5
Therefore, she will be approximately 44.5 years old when the retirement fund has an accumulated value of $1,000,000.
To find out how old the girl will be when the fund has an accumulated value of $1,000,000, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A is the final amount (in this case, $1,000,000)
P is the principal amount (initial deposit)
r is the annual interest rate (15%, or 0.15)
n is the number of times interest is compounded per year
t is the number of years
Since the girl plans to deposit $2,000 at the end of each year, we can assume that the principal amount is $2,000.
Let's plug the values into the formula and solve for t:
$1,000,000 = $2,000(1 + 0.15/n)^(nt)
To make things simpler, let's assume that the interest is compounded annually (n = 1):
$1,000,000 = $2,000(1 + 0.15/1)^(t*1)
Simplifying the equation:
$1,000,000 = $2,000(1.15)^t
Dividing both sides by $2,000:
500 = 1.15^t
Now we need to solve for t, the number of years. We can do this by taking the natural logarithm (ln) of both sides of the equation:
ln(500) = ln(1.15^t)
Using the property of logarithms (ln of a power):
ln(500) = t * ln(1.15)
To solve for t, divide both sides by ln(1.15):
t = ln(500) / ln(1.15)
Using a calculator, we find that t is approximately 38.396 years.
Therefore, when the retirement fund has an accumulated value of $1,000,000, the girl will be approximately 22 + 38.396 = 60.396 years old.
So she will be about 60 years old when the fund reaches $1,000,000.