# Math

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...)

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1. 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

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