please help

Question

 

A $2500 investment is made at a 5% annual interest rate compounded continuously.

Use the compound interest formula for continuous compounded interest to determine how long it would take

for the balance in the account to reach $5000. Round your answer to the nearest tenth of a year.

Answer 1

The formula for continuous interest is a bit different to the formulas (formulae?) for other kinds of compound interest.  It is:

 

Final Amount = Starting Amount * e^rt

 

or

 

A = Pe^rt

 

as a review, 'e' is a constant, like pi.  The value of 'e' is approx 2.718

 

so

 

we want to solve for 't' (time) which means rearranging this a bit:

A/P = e^rt

 

ln(A/P) = ln(e^rt)

 

one of our log identities tells us that

 

ln(e^rt) = rt*ln(e)

 

ln (e) = 1

 

SO

 

t = ln (A/P) / r

t = ln (5000/2500) / .05

 

t = ln(2) / .05

t = approx 13.86, which rounds to 13.9 years