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: 1.3%

Step-by-step explanation:

To find rate of interest (r) per annum for a fund deposit by depositor .

Initial saving payment  P= $1,000

Amount after three years A =$1,040.40

we know that

$A=P(1+\frac{r}{100} )^n\\\\\Rightarrow\ 1040=1000(1+\frac{r}{100} )^3\\\Rightarrow\ \frac{1040}{1000} =(1+\frac{r}{100} )^3\\\Rightarrow\ 1.040=(1+\frac{r}{100} )^3\\\text{by taking log on both sides we get,}\\log(1.040)=log((1+\frac{r}{100} )^3)\\\Rightarrow\ 0.039=3log(1+\frac{r}{100})\\\Rightarrow\ 0.013=log(1+\frac{r}{100})\\\Rightarrow\ e^0.013=1+\frac{r}{100}\\\Rightarrow\ 1.013=(1+\frac{r}{100})\\\Rightarrow\ 1.013-1=\frac{r}{100}$

r=0.013×100=1.3%