5. An $800 deposit for 24months earned $200 ininterest

Answer:The rate of interest applied fro compound interest is 24.5 %  The rate of interest applied simple interest is 37.5 %Step-by-step explanation:Given as :The Principal amount that is deposited = $ 800The Time period = 24 months = 2 yearsThe Interest earn = $ 200Let the rate of interest = R %So, The Amount = Principal deposited - interest earnOr, A = $ 800 - $ 200∴ Amount = $ 600From compounded methodAmount = Principal × [tex](1+\dfrac{\textrm rate}{100})^{\textrm Time}[/tex]Or, $ 600 = $ 200 × [tex](1+\dfrac{\textrm R}{100})^{\textrm 2}[/tex]Or, [tex]\frac{600}{200}[/tex] = [tex](1+\dfrac{\textrm R}{100})^{\textrm 2}[/tex]Or, 3 = [tex](1+\dfrac{\textrm R}{100})^{\textrm 2}[/tex]Or, [tex]3^{\frac{1}{2}}[/tex] = (1 +[tex]\frac{R}{100}[/tex])Or, 1.245 = (1 +[tex]\frac{R}{100}[/tex])or, 1.245 - 1 = [tex]\dfrac{R}{100}[/tex]or, 0.245 × 100 = RSo, the rate is = 24.5 %Hence The rate of interest applied fro compound interest is 24.5 %  AnswerFrom Simple Interest method Simple Interest = [tex]\dfrac{\textrm Principal\times \textrm Rate\times \textrm Time}{100}[/tex]Or, $ 600 = [tex]\dfrac{\textrm 800\times \textrm R\times \textrm 2}{100}[/tex]Or,  $ 600 × 100 = $ 800 × R × 2Or, R = [tex]\frac{60000}{1600}[/tex]∴ R = 37.5 %So, The rate is 37.5 %Hence The rate of interest applied simple interest is 37.5 %Answer