Answer:
The rate of interest per annum is 1.3%.
Step-by-step explanation:
Given Principal P = $1000
time period n = 3
Amount A = $1039.90 ≈ $1040
To find rate (r) of interest per annum
We know that :
[tex]A = P\cdot (1+\frac{rate}{n})^{n\cdot time}\text{ ; where n is no. of times the interest is compounded annualy}\\\\\implies1040=1000\cdot (1+\frac{rate}{100})^3\\\\\implies 1.040=(1+\frac{r}{100})^3\\\\\text{Taking log on both the sides}\\\implies log(1.040)=3\cdot log(1+\frac{r}{100})\\\\\implies0.039=3\cdot log(1+\frac{r}{100})\\\\\implies 0.013=log(1+\frac{r}{100})\\\\\implies e^{0.013}=(1+\frac{r}{100})\\\\\implies r=0.013=1.3\%[/tex]
⇒ interest rate per annum = 1.3%.
