You deposit $1200 in an account that pays an APR of 7% compounded monthly. How long will it take for your balance to reach $150,000?
im not really sure but maybe itslike a month because the way I put it in my calculator Is
1200/0.07=17142.85714
but im not good at math so idk. I tried at least
I assume you are depositing the $1200 every month
monthly rate = .07/12 = .00583333..
number of months = n
1200( 1.0058333..^n - 1)/.0058333 = 150000
( 1.0058333..^n - 1)/.0058333 = 125
1.0058333^n - 1 = .72916662..
1.00583333^n = 1.72916662...
take log of both sides
log 1.00583333^n = log 1.72916662...
nlog 1.00583333 = log 1.72916662...
n = log 1.72916662.../log 1.00583333
n = 94.15 monts
n = appr 94 months or 7 years and 10 months
To calculate the time it will take for your balance to reach $150,000, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future balance you want to achieve ($150,000 in this case)
P = the initial deposit amount ($1200 in this case)
r = the annual interest rate (7% or 0.07 in decimal form)
n = the number of compounding periods per year (since it's compounded monthly, n = 12)
t = the time in years (what we want to find)
Now, let's plug in the values we have and solve for t:
$150,000 = $1200(1 + 0.07/12)^(12t)
Divide both sides of the equation by $1200:
125 = (1 + 0.07/12)^(12t)
Take the natural logarithm of both sides:
ln(125) = ln((1 + 0.07/12)^(12t))
Use the properties of logarithms to bring down the exponent:
ln(125) = 12t * ln(1 + 0.07/12)
Finally, divide both sides by 12 * ln(1 + 0.07/12):
t = ln(125) / (12 * ln(1 + 0.07/12))
Using a calculator, we can find that t ≈ 21.79 years.
Therefore, it will take approximately 21.79 years for your balance to reach $150,000 if you deposit $1200 in an account that pays an APR of 7% compounded monthly.