How long would it take to accumulate $2,000,000 at a rate of 5% with the starting amount of $1,150,
To calculate how long it would take to accumulate $2,000,000 at a rate of 5% starting from $1,150, we can use the formula for compound interest.
The formula for compound interest is given by:
P = A(1 + r/n)^(nt)
Where:
P = the future value of the investment/loan (in this case $2,000,000)
A = the starting amount (in this case $1,150)
r = the annual interest rate (in this case 5%, which is equivalent to 0.05)
n = the number of times that interest is compounded per year (assuming annually, so n = 1)
t = the number of years
Rearranging the formula to solve for t:
t = (ln(P/A))/(n * ln(1 + r/n))
Plugging in the values into the formula:
t = (ln(2,000,000/1,150))/(1 * ln(1 + 0.05/1))
Calculating the natural logarithm:
t ≈ (ln(1,739.13))/ln(1.05)
Simplifying the equation:
t ≈ 7.18/0.0488
Finally, calculating t:
t ≈ 147.13
Therefore, it would take approximately 147.13 years to accumulate $2,000,000 starting from $1,150 at an interest rate of 5% compounded annually.