Question

The formula for continuously compounded interest on a principal investment Pat a given interest rater

over time tin years is given by A = Per? You have deposited $12,000 in an account that pays 4.15%
interest, compounded continuously. How long will it take for your initial investment to grow six times its
original worth? Round your answer to the nearest tenth.

Answer 1

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.