Suppose that i sub $n = 5%$ for all $n ≥ 1$. How long will it take an investment to triple in value?

Question

Suppose that i sub $n = 5%$ for all $n ≥ 1$. How long will it take an investment to triple in value?

I tried to use $3x=x(e^{.05t})$

then i got $\ln3+\ln x=\ln x+.05t$

so $t=\ln(3)/.05 = 21.97$

but i know that the answer is $22.5171$

Answer 1

The discrepancy in the value is due to the use of continuous compounding than the discrete compounding.

So $3X = X(1+.05)^t$

Taking logarithm on both sides, you get $\ln(3) = t\ln(1.05)$

$t = \ln(3)/\ln(1.05) = 22.5171$

There you go!!

I still wonder what n is? and x_n is ?

Goodluck