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Sagot :
We need to find the greatest interest in given options.
Let the principal amount be, P= $100.
The number of years, t =1
Consider the individual options.
a)
Simple interest,r = 5.0 % =0.05.
Consider the formula to find the simple interest.
[tex]SI=Prt[/tex]Substitute P=100, r =0.05 and t=1 in the equation.
[tex]SI=100\times0.05\times1[/tex][tex]SI=\text{ \$}5[/tex]b).
Compound interest, r =5.0% =0.05.
n=4.
Consider the formula to find the compound interest.
[tex]CI=P(1+\frac{r}{n})^{nt}-P[/tex]Substitute n=4, P=100, r =0.05 and t=1 in the equation.
[tex]CI=100(1+\frac{0.05}{4})^{4\times1}-100[/tex][tex]CI=\text{ \$}5.094[/tex]c).
Compound interest, r =5.0% =0.05.
n=12.
Consider the formula to find the compound interest.
[tex]CI=P(1+\frac{r}{n})^{nt}-P[/tex]Substitute n=12, P=100, r =0.05 and t=1 in the equation.
[tex]CI_1=100(1+\frac{0.05}{12})^{12\times1}-100[/tex][tex]CI_1=\text{ \$}5.116[/tex]We know that
[tex]5.116>5.094>5[/tex][tex]CI_1>CI>SI[/tex]5.0% interest compounded monthly will return the greatest interest.
Final answer:
5.0% interest compounded monthly
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