Calculate How Long Your Money Was in the Bank
Explanation:
To calculate the amount of time it takes for your money to reach $28,000 with an interest rate of 6% compounded continuously, we can use the continuous compounding formula:
A = P * e^(rt)
Where:
A is the final amount of money, which is $28,000
P is the principal balance, which is $20,000
e is the mathematical constant approximately equal to 2.71828
r is the interest rate per year, which is 6% or 0.06 as a decimal
t is the time in years that the money is left in the bank and needs to be calculated
Substituting the given values, we get:
$28,000 = $20,000 * e^(0.06t)
To solve for t, we can divide both sides of the equation by $20,000 and then take the natural logarithm of both sides:
ln($28,000/$20,000) = 0.06t
t = ln(1.4) / 0.06 â 7.578 years
Rounding to the nearest tenth, the answer is D) 7.6 years.