To find out how many years it will take for an initial investment of $19,000 to grow to $33,800 compounded daily at 12% APR, we can use the formula for compound interest. Plugging in the values and solving for t, we find that it will take approximately 3.6 years for the initial investment to grow to the desired amount.
To find out how many years it will take for an initial investment of $19,000 to grow to $33,800 compounded daily at 12% APR, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A is the final amount
P is the principal amount (initial investment)
r is the annual interest rate (in decimal form)
n is the number of times the interest is compounded per year
t is the number of years
Plugging in the values:
33,800 = 19,000(1 + 0.12/365)^(365t)
Now, we can solve for t by isolating it:
1.78 = (1 + 0.0003288)^(365t)
Now, take the natural logarithm of both sides:
ln(1.78) = ln((1 + 0.0003288)^(365t))
Using logarithm properties, we can move the exponent down:
ln(1.78) = 365t * ln(1 + 0.0003288)
Divide both sides by 365 * ln(1 + 0.0003288):
t = ln(1.78) / (365 * ln(1 + 0.0003288))
Using a calculator, we find that t is approximately 3.6 years. Therefore, it will take approximately 3.6 years for the initial investment of $19,000 to grow to $33,800 compounded daily at 12% APR.