Question

How long will it take ₱10,000 to accumulate to the amount of ₱11,000 at 12% compounded monthly?

Answer 1

Hello

To solve this question, we would need to use the forumla of compound interest

`\begin{gathered} p=10,000 \\ a=11,000 \\ r=12\text{ \%=0.12} \\ t=\text{ ?} \\ n=12 \end{gathered}`

Let's input the data into the forumla

`\begin{gathered} a=p(1+(r)/(n))^(nt) \\ 11000=10000(1+(0.12)/(12))^(12* t) \\ (11000)/(10000)=(1+0.01)^(12t) \\ 1.1=1.01^(12t) \\ \text{take log of both sides} \\ \log 1.1=12t\log 1.01 \\ 12t=(\log 1.1)/(\log 1.01) \\ 12t=9.579 \\ (12t)/(12)=(9.579)/(12) \\ t=0.798\text{years} \end{gathered}`

This can be converted to months

`\begin{gathered} 12\text{months}=1\text{year} \\ x=0.798 \\ x=12*0.798 \\ x=9.579\text{ months} \\ x\approx10\text{months} \end{gathered}`

It would take approximately 10 months to get 11,000 from a principal of 10,000 at a rate of 12%