1.Find the amount in an account where $200 is invested at 3.5% compounded quarterly for a period of 3 years.2.Find the amount in an account where $200 is invested at 3.5% compounded continuously for a period of 3 years.Each answer must include the intermediate steps used to arrive at the answer.
Accepted Solution
A:
Part 1 :P = $200r = 3.5% or 0.035t = 3n = 4Compound interest formula = [tex]P(1+\frac{r}{n})^{nt}[/tex]= [tex]200(1+\frac{0.035}{4})^{3*4}[/tex]= [tex]200(1.00875)^{12}[/tex] = [tex]200\times1.1102[/tex]= 222.04So, money in the bank will be = 200+222.04 = $422.04Part 2 :P = $200r = 3.5% or 0.035t = 3Continuous compound interest formula is = A = [tex]Pe^{rt}[/tex]Putting e = 2.71828 we get.A = [tex]200(2.71828)^{0.035*3}[/tex]= [tex]200(2.71828)^{0.105}[/tex]= 200*1.11071 = 222.14Hence, amount in account after 3 years will be= 200+222.14 = $422.14