Question

Compare the future amounts (A) you would have if the money were invested at simple interest and if it were invested with annual compounding. (Round your answer to the nearest cent.)$6,100 at 14% for 30 years Simple interest A=$31720Compound interest A=?

Answer 1

Step 1

Write the expression for simple interest and compound interest.

`\begin{gathered} \text{For simple interest} \\ Interest(I)=(Principal(P)* Rate(R)* Time(T))/(100) \\ \text{Where} \\ P=\text{\$}6100 \\ R=14 \\ T=\text{ 30} \end{gathered}`
`\begin{gathered} \text{For compound interest} \\ A=P(1+(R)/(n))^(nt) \\ \text{Where} \\ P=\text{principal=\$6100} \\ R=\text{ rate}=(14)/(100)=0.14 \\ n=\text{ number of times interest is applied per time period}=1 \\ t=number\text{ of times period elasped}=30 \end{gathered}`

Step 2

Find the simple interest and compound interest and compare them

`\begin{gathered} \text{For the simple interest} \\ I=(6100*14*30)/(100) \\ I=\text{\$}25620 \\ \text{Amount = principal + interest=\$6100+\$25620=\$31720} \end{gathered}`
`\begin{gathered} \text{For the Compound interest} \\ \text{Amount = A} \\ A=6100(1+(0.14)/(1))^(1*30) \\ A=6100(1+0.14)^(30) \\ A=6100(1.14)^(30) \\ A=\text{\$}310,795.9674 \\ \end{gathered}`

Therefore, the future amount based on simple interest =$31720, and the future amount based on compound interest =$310,795.9674. To the nearest cents $310,795.97 for the amount based on compound interest and $31720.00 for the amount based on simple interest