We know that, Amount in Compound interest is given by :
[tex]\bigstar \ \ \boxed{\sf{Amount = Principal\bigg(1 + \dfrac{Rate \ of \ Interest}{100}\bigg)^{Time \ Period}}}[/tex]
Given : Principal = $2000
Given : Annual yield is 5% and the interest is compounded quarterly
It means : Interest is compounded 4 times in a year
[tex]\implies \sf{Rate \ of \ Interest = \dfrac{R}{4} = \dfrac{5}{4}}[/tex]
[tex]\sf{\implies Time \ period = (25 \times 4) = 100}[/tex]
Substituting all the values in the formula, we get :
[tex]\implies \sf{Amount = 2000\bigg(1 + \dfrac{\dfrac{5}{4}}{100}\bigg)^{100}}[/tex]
[tex]\implies \sf{Amount = 2000\bigg(1 + \dfrac{5}{400}\bigg)^{100}}[/tex]
[tex]\implies \sf{Amount = 2000\bigg(1 + \dfrac{1}{80}\bigg)^{100}}[/tex]
[tex]\implies \sf{Amount = 2000\bigg(\dfrac{81}{80}\bigg)^{100}}[/tex]
[tex]\implies \sf{Amount = 2000 \times (1.0125)^{100}}[/tex]
[tex]\implies \sf{Amount = 2000 \times 3.463}}[/tex]
[tex]\implies \sf{Amount = 6926.8}[/tex]
