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What is the exact time t, in years, needed for the balance of an account that earns 5% annual 8. Interest compounded continuously to triple?

User Badzil
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Answer:

It takes 22.52 years for the balance to triple in value.

Explanation:

Continuous compounding:

The amount of money earned using continuous compounding is given by the following equation:


A(t) = A(0)(1+r)^t

In which A(0) is the initial amount of money and r is the interest rate, as a decimal.

Interest rate of 5%.

This means that
r = 0.05, and thus:


A(t) = A(0)(1+r)^t


A(t) = A(0)(1+0.05)^t


A(t) = A(0)(1.05)^t

Time for the balance to triple?

This is t for which
A(t) = 3A(0). So


A(t) = A(0)(1.05)^t


3A(0) = A(0)(1.05)^t


(1.05)^t = 3


\log{(1.05)^t} = \log{3}


t\log{1.05} = \log{3}


t = \frac{\log{3}}{\log{1.05}}


t =  22.52

It takes 22.52 years for the balance to triple in value.

User Mihir Oza
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