Question

Lisa invested 5300 in the account that pays annual interest rate of 2.5%, compounded monthly. Find the effective annual interest rate, express as a percentage. Do not round any intermediate computations, and round your answer to the nearest hundredth

Answer 1

Solution

Given

Principal: $5300

rate: 2.5% = 0.025

n = 12

t = 1

a)

$\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ \\ \Rightarrow A=5300(1+\frac{0.025}{12})^{12\times1}=\ 5434.03 \end{gathered}$

b)

The effective annual interest is;

$\begin{gathered} EAR=(1+\frac{r}{n})^n-1 \\ \\ \Rightarrow EAR=(1+\frac{0.025}{12})^{12}-1=0.025288=2.53\% \end{gathered}$