Question
Determine how much time is required for an investment to quadruple if interest is earned at a rate of 7.1% compounded continously.
(no other info is given, and that's why I'm confused...)
(no other info is given, and that's why I'm confused...)
Answers
MathMate
When no other info is given, you can start with an arbitrary amount, say $1000, or simply $1.
The question reduces to:
In how many years will $1 grow to $4 if the interest is compounded continuously at 7.1% p.a.
The accumulation function for interest compounded continuously is
a(t)=e^(rt)
where a(t) is the future value of $1 compounded at an interest rate of r for t years. E is the base of natural log, equal to approximately 2.7182818284...
In the present case,
we have
4=e^(0.071t)
Take natural log on both sides and solve for t:
t=ln(4)/0.071
=19.525 years
The question reduces to:
In how many years will $1 grow to $4 if the interest is compounded continuously at 7.1% p.a.
The accumulation function for interest compounded continuously is
a(t)=e^(rt)
where a(t) is the future value of $1 compounded at an interest rate of r for t years. E is the base of natural log, equal to approximately 2.7182818284...
In the present case,
we have
4=e^(0.071t)
Take natural log on both sides and solve for t:
t=ln(4)/0.071
=19.525 years