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Sagot :
Statement Problem: You are given the choice of taking the simple interest on $100,000 invested for 3 years at a rate of 5% or the interest on $100,000 invested for three years at an interest of 5% compounded monthly. Which investment earns the greater amount of interest? Given the difference between the amounts of interest earned bu the two investments.
Solution:
The simple interest of an amount invested P fot time t at a rate of r is calculated using;
[tex]I=Prt[/tex]Thus, the interest is;
[tex]\begin{gathered} P=100,000,r=0.05,t=3 \\ I=100000\times0.05\times3 \\ I=15000 \end{gathered}[/tex]The interest earned using simple interest is $15,000.
The amount earned using compound interest is;
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt}_{} \\ P=100000,r=0.05,t=3,n=12(\text{monthly)} \\ A=100000(1+\frac{0.05}{12})^{12(3)} \\ A=116147.22 \end{gathered}[/tex]But the interest earned is the difference between the total amount earned and the invested amount. We have;
[tex]\begin{gathered} I=A-P \\ I=116147.22-100000 \\ I=16147.22 \end{gathered}[/tex]The interest earned using compound interest is $16,147.22
CORRECT ANSWER: The investment with the compound interest earns greater amount of interest.
The difference between the amounts of interest earned by the two investments is;
[tex]16147.22-15000=1147.22[/tex]The difference between the amounts of interest earned by the two investments is $1,147.22
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