you have $42,180.53 in a brokeage act & you plan to deposit an additional $5000 at the end of every future year until your accout totals $250,000.
you expect to earn 12% annually on the account. How many years will it take to reach your goal?
To calculate how many years it will take to reach your goal, we can use the future value of an annuity formula. The formula is:
FV = P * (1 + r)^n - 1 / r
Where:
FV = Future value (desired goal)
P = Yearly deposit
r = Annual interest rate
n = Number of years
In this case:
FV = $250,000
P = $5,000
r = 12% or 0.12 (convert percentage to decimal)
Plugging these values into the formula, we get:
$250,000 = $5,000 * (1 + 0.12)^n - 1 / 0.12
Dividing both sides by $5,000:
50 = (1.12)^n - 1 / 0.12
To solve for n (the number of years), we can use logarithms. Taking the natural logarithm (ln) of both sides:
ln(50) = ln((1.12)^n - 1 / 0.12)
Using the property of logarithms, we can simplify this to:
ln(50) = n * ln(1.12) - ln(0.12)
Now we can solve for n. Using a calculator, evaluate ln(1.12):
ln(50) = n * 0.112 + ln(0.12)
Rearranging the equation to solve for n:
n * 0.112 = ln(50) - ln(0.12)
Dividing both sides by 0.112:
n = (ln(50) - ln(0.12)) / 0.112
n ≈ 26.43
Therefore, it will take approximately 26.43 years to reach your goal of $250,000 with an annual deposit of $5,000 and an annual interest rate of 12%.
To determine how many years it will take to reach the goal of $250,000, we can use the future value of an ordinary annuity formula. The formula is as follows:
FV = P * [(1 + r)^n - 1] / r
Where:
FV = Future value of the annuity (in this case, $250,000)
P = Payment made at the end of each period (in this case, $5,000)
r = Interest rate per period (in this case, 12% or 0.12)
n = Number of periods
We can rearrange the formula to solve for n:
n = log((FV * r / P) + 1) / log(1 + r)
Let's plug in the numbers:
FV = $250,000
P = $5,000
r = 0.12
n = log((250000 * 0.12 / 5000) + 1) / log(1 + 0.12)
Using a calculator, the result is approximately 14.66.
Since the number of years must be a whole number, we round up to 15 years.
Therefore, it will take approximately 15 years to reach your goal of $250,000 with an annual deposit of $5,000 and 12% annual interest.