Respuesta :
Answer: [tex]\begin{gathered} a)\text{ \$49902.61} \\ b)\text{ \$50051.31} \\ c)\text{ \$50179.32} \\ d)\text{ \$50204.53} \end{gathered}[/tex]Explanation:
Amount invested = $39,100
rate = 5% = 0.05
t = Time = 5 years
To determine the compounding methods, we will apply the compound interest formula:
[tex]$FV\text{ = P(1 +}\frac{r}{n})^{nt}$[/tex][tex]\begin{gathered} a)\text{ Annual compounding:} \\ n\text{ = number of times compounded = annual} \\ n\text{ = 1} \\ FV\text{ = 39100\lparen1 + }\frac{0.05}{1})^{1\times5} \\ FV=\text{ 39000\lparen1.05\rparen}^5 \\ FV=\text{ 49902.61} \\ To\text{ the nearest penny, the future value is \$49902.61} \end{gathered}[/tex][tex]\begin{gathered} b)\text{ Semi-annual compounding:} \\ n\text{ = 2} \\ FV\text{ = 39100\lparen1 + }\frac{0.05}{2})^{2\times5} \\ FV=\text{ 39000\lparen1.025\rparen}^{10} \\ FV=\text{ 50051.31} \\ To\text{ the nearest penny, the future value is \$50051.31} \end{gathered}[/tex][tex]\begin{gathered} c)\text{ Monthly compounding:} \\ n\text{ = 12} \\ FV\text{ = 39100\lparen1 + }\frac{0.05}{12})^{12\times5} \\ FV=\text{ 39100\lparen1.00417\rparen}^{60} \\ FV=\text{ 50179.32} \\ To\text{ the nearest penny, the future value is \$50179.32} \end{gathered}[/tex][tex]\begin{gathered} d)\text{ }Daily\text{ compounding:} \\ n\text{ = 365} \\ FV\text{ = 39100\lparen1 + }\frac{0.05}{365})^{365\times5} \\ FV=50204.53 \\ To\text{ the nearest penny, the future value is \$50204.53} \end{gathered}[/tex]