Sara has $2,500,000 and can earn 12.50 percent per year. If Sara plans on retiring when she has tripled her money, she can retire in how many years.
If she has 2500,000 and she gets 12.5% per year in interest, she would earn $312,500 per year right now.
Heck!, she should retire right now
but according to your question
2.5 million(1.125)^n = 7.5 million
1.125)^n = 3
n log 1.123 = log3
n = appr 9.3 years
To find out how long it will take for Sara to triple her money, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the amount after time t
P = the initial principal (in this case, $2,500,000)
r = annual interest rate (in decimal form, 12.50% = 0.125)
n = number of times interest is compounded per year (we'll assume it's compounded annually)
t = time in years
We want to find t when A = 3P (triple the initial principal).
3P = P(1 + r/n)^(nt)
Dividing both sides by P, we get:
3 = (1 + r/n)^(nt)
Taking the logarithm of both sides:
log(3) = log[(1 + r/n)^(nt)]
Using the property of logarithms, we can bring the exponent down:
log(3) = nt * log(1 + r/n)
We can now solve for t:
t = log(3) / (n * log(1 + r/n))
Since interest is compounded annually (n = 1) and the annual interest rate is 12.50% (r = 0.125), we can substitute these values into the equation:
t = log(3) / (1 * log(1 + 0.125/1))
Calculating the expression:
t = log(3) / log(1.125)
t ≈ log(3) / 0.0492
Using a calculator, we find:
t ≈ 6.956
Therefore, Sara can retire in approximately 6.956 years when she has tripled her money.
To determine the number of years Sara can retire, we need to calculate how long it will take for her initial investment to triple at an annual interest rate of 12.50 percent.
Let's break down the problem step by step:
Step 1: Find the end goal amount.
To triple the initial investment of $2,500,000, we need to multiply it by 3:
End goal amount = $2,500,000 * 3 = $7,500,000.
Step 2: Calculate the number of years required to reach the end goal.
The formula for calculating compound interest is:
End value = Principal * (1 + interest rate)^time.
In this case, the principal is $2,500,000, and the interest rate is 12.50 percent or 0.125.
So, we can rewrite the formula as:
$7,500,000 = $2,500,000 * (1 + 0.125)^time.
Step 3: Solve for time.
Divide both sides of the equation by $2,500,000:
(1 + 0.125)^time = 7,500,000 / 2,500,000.
Now, we can take the logarithm of both sides to solve for time:
log((1 + 0.125)^time) = log(7,500,000 / 2,500,000).
Using the logarithm identity, log(a^b) = b * log(a), we can rewrite the equation as:
time * log(1 + 0.125) = log(7,500,000 / 2,500,000).
Finally, we can solve for time by dividing both sides of the equation by log(1 + 0.125):
time = log(7,500,000 / 2,500,000) / log(1 + 0.125).
Using a calculator, we can find the value of time. Plugging in the numbers:
time ≈ 20.56 years.
Therefore, Sara can retire in approximately 20.56 years.