Question

What interest rate per annum is a fund paying its clients if the third to the last payment of a depositor became Php 1,040.40 from an initial savings payment of Php 1,000.00?

Answer 1

Answer: The rate of interest per annum is 1.3%.

Step-by-step explanation:

Given  Principal P= $1000

time period n=3

Amount A=$1040,40

To find rate of interest per annum r

We know that

$A=P(1+\frac{r}{100} )^3\\\Rightarrow\ 1040=1000(1+\frac{r}{100})^3\\\Rightarrow\ 1.040=(1+\frac{r}{100})^3\\\text{taking log on both sides}\\log(1.040)=3log(1+\frac{r}{100})\\\Rightarrow0.039=3log(1+\frac{r}{100})\\\Rightarrow0.013=log(1+\frac{r}{100})\\\\\Rightarrow\ e^{0.013}=(1+\frac{r}{100})\\\Rightarrow\ 1.013=(1+\frac{r}{100})\\\Rightarrow\ \frac{r}{100}=1.013-1=0.013$

⇒  r = 1.3%.