Respuesta :
[tex]\text{The amount in an account compounding interest rate is given by}\\ \\ A=P\left ( 1+\frac{r}{n} \right )^{nt}\\ \\ \text{here A is amount after t year, P is the principal amount, r is interest}\\ \text{rate in decimals, n is the number of times compounded in a year.}[/tex]
here we have given that currently amount is A=$ 3981.04
the account opened with a principle amount, P=$ 3760.19
[tex]\text{ the interest compounded daily, so }n=365\\ \text{and the time is t=5 years. so let the interest rate is r. so}\\ \\ A=P\left ( 1+\frac{r}{n} \right )^{nt}\\ \\ 3981.04=3760.19\left ( 1+\frac{r}{365} \right )^{365(5)}[/tex]
[tex]\Rightarrow \frac{3981.04}{3760.19}=\left ( 1+\frac{r}{365} \right )^{1825}\\ \\ \Rightarrow 1.0587=\left ( 1+\frac{r}{365} \right )^{1825}\\ \\ \Rightarrow \left ( 1+\frac{r}{365} \right )^{1825}=1.0587\\ \\ \Rightarrow \left ( 1+\frac{r}{365} \right )=(1.0587)^{\frac{1}{1825}}[/tex][tex]\Rightarrow 1+\frac{r}{365} \approx 1.0000313\\ \\ \Rightarrow \frac{r}{365}=1.0000313-1\\ \\ \Rightarrow \frac{r}{365}=0.0000313\\ \\ \Rightarrow r=0.0000313\times 365\\ \\ \Rightarrow r\approx 0.011[/tex]
Hence the interest rate on the account is: 1.1%
