Answer:
43.2 years
Explanation:
The formula for continuously compounded interest on a principal investment Pat a given interest rater
over time tin years is given by A = Pe^rt
P = Initial amount compounded = $12000
A = Amount compounded continuously after t years = six times it's original worth
= 6 × $12,000 = $72000
r = Interest rate = 4.15%
t = time in years = ?
Making t the subject of the formula
t = ln(A/P) / r
First, convert R percent to r a decimal
r = R/100
r = 4.15%/100
r = 0.0415 per year,
Then, solve our equation for t
t = ln(A/P) / r
t = ln(72,000.00/12,000.00) / 0.0415
t = 43.175 years
Approximately t = 43.2 years
The time required to get a total amount of $ 72,000.00 from compound interest on a principal of $ 12,000.00 at an interest rate of 4.15% per year and compounded continuously is 43.2years.