Respuesta :
Answer:
Therefore total amount after [tex]5 \ years[/tex] at the rate of [tex]0.5[/tex]% is [tex]1025\ dollars[/tex].
Therefore total amount after [tex]5 \ years[/tex] at the rate of [tex]0.75[/tex]% is [tex]1038\ dollars[/tex].
Step-by-step explanation:
Given that,
Principle Amount [tex](P)= 1000\ dollars[/tex], Time [tex]=[/tex] [tex]5\ years[/tex] and he is considering two investment options. According to his investment options, Rate of simple interest for option [tex]A[/tex] is [tex]0.5[/tex]% and Rate of compounded Interest for option [tex]B[/tex] is [tex]0.75[/tex]%.
Now, considering option [tex]A[/tex].
Principle Amount [tex](P)= 1000\ dollars[/tex]
Time [tex]=[/tex] [tex]5\ years[/tex]
Rate of Interest [tex]=0.5[/tex]%
Simple Interest [tex]=(SI)=\frac{P\times R\times\ T}{100}[/tex]
[tex]=\frac{1000\times 0.5\times 5}{100}[/tex]
[tex]=\frac{2500}{100}[/tex]
[tex]=25[/tex]
Total Amount [tex](A)=[/tex] Principle Amount [tex](P)+[/tex] Simple Interest [tex](SI)[/tex]
[tex]= 1000+25[/tex]
[tex]=1025[/tex]
Therefore total amount after [tex]5 \ years[/tex] at the rate of [tex]0.5[/tex]% is [tex]1025\ dollars[/tex].
Now, considering option [tex]B[/tex].
Principle Amount [tex](P)= 1000\ dollars[/tex]
Time [tex]=[/tex] [tex]5\ years[/tex]
Rate of Interest [tex]=0.75[/tex]%
Total Amount after [tex]5\ years[/tex] [tex]= P(1+\frac{R}{100} )^{5}[/tex]
[tex]=1000(1+\frac{0.75}{100} )^{5}[/tex]
[tex]= 1000(1.0075)^{5}[/tex]
[tex]=1000\times 1.0380[/tex]
[tex]=1038.06[/tex]
Therefore total amount after [tex]5 \ years[/tex] at the rate of [tex]0.75[/tex]% is [tex]1038\ dollars[/tex].
