# An investment

How long will it take for an investment to double at a simple interest rate of 5.10% p. A. ?
Express the answer in years and months, rounded up to the next month.

Correct result:

y =  1
m =  2

#### Solution:

$p=1 + \dfrac{ 5.10 }{ 100 }=1.051 \ \\ \ \\ p^n=2 \ \\ n \ln p=\ln 2 \ \\ n=\ln(2) / \ln(p)=\ln(2) / \ln(1.051) \doteq 13.9348 \ \\ \ \\ n_{1}=\lceil n \rceil=\lceil 13.9348 \rceil=14 \ \\ \ \\ y=\lfloor n_{1} / 12 \rfloor=\lfloor 14 / 12 \rfloor=1$
$m=n_{1} - 12 \cdot \ y=14 - 12 \cdot \ 1=2$

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