If $9,400 is invested at an interest rate of 8% per year, find the value of the investment at the end of 5 years if interested is compounded annually (once a year), semiannually (twice a year), monthly (12 times a year), daily (assume 365 days a year), or continuously. Round to the nearest cent. For each, use the correct compound interest formula from the following. A = P ( 1 + r n ) n t or A = P e r t(a) Annual:(b) Semiannual:(c) Monthly:(d) Daily:(e) Continuously:

Answer:(a) $13811.68(b) $13914.30(c) $14004.55(d) $14022.54(e) $14023.15Step-by-step explanation:Since, the amount formula in compound interest,[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Where,P = Principal amount,r = annual rate,n = number of periods,t = number of years,Here, P = $ 9,400, r = 8% = 0.08, t = 5 years, If the amount is compounded annually,n = 1,Hence, the amount of investment would be, [tex]A=9400(1+\frac{0.08}{1})^5=9400(1.08)^5=\$ 13811.6839219\approx \$ 13811.68[/tex](a) If the amount is compounded annually,n = 1,The amount of investment would be, [tex]A=9400(1+\frac{0.08}{1})^5=9400(1.08)^5=\$ 13811.6839219\approx \$ 13811.68[/tex](b) If the amount is compounded semiannually,n = 2,The amount of investment would be, [tex]A=9400(1+\frac{0.08}{2})^{10}=9400(1.04)^{10}=\$13914.2962782\approx \$ 13914.30[/tex](c) If the amount is compounded Monthly,n = 12,The amount of investment would be, [tex]A=9400(1+\frac{0.08}{12})^{60}=9400(1+\frac{1}{150})^{60}=\$ 14004.549658\approx \$ 14004.55[/tex](d) If the amount is compounded Daily,n = 365,The amount of investment would be, [tex]A=9400(1+\frac{0.08}{365})^{365\times 5}=9400(1+\frac{2}{9125})^{1825}=\$ 14022.5375476\approx \$ 14022.54[/tex](e) Now, the amount in compound continuously,[tex]A=Pe^{rt}[/tex]Where, P = principal amount,r = annual rate,t = number of years,So, the investment would be,[tex]A=9400 e^{0.08\times 5}=9400 e^{0.4}=\$14023.1521578\approx \$14023.15[/tex]