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Sagot :
Answer:
a) Future value = $11,749.38
Interest = $2,844.82
b) Future value = $11,717.79
Interest = $2,813.23
Explanations:
The formula for calculating the future amount (compound amount) is expressed as;
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ \end{gathered}[/tex]P is the amount invested
r is the rate (in decimal)
n is the compounding time
t is the time (in years)
Given the following parameters:
[tex]\begin{gathered} P=$\$8904.56$ \\ t=7\text{years} \\ n=2(semi-annually) \\ r=4\%=0.04 \end{gathered}[/tex]Substitute the given parameters into the formula:
[tex]\begin{gathered} A=8904.56(1+\frac{0.04}{2})^{2(7)} \\ A=8904.56(1+0.02)^{14} \\ A=8904.56(1.02)^{14} \\ A=8904.56(1.3195) \\ A\approx\$11,749.38 \end{gathered}[/tex]Hence the future value if the amount invested is compounded semiannually is approximately $11,749.38
Calculate the interest;
[tex]\begin{gathered} A=P+I \\ I=A-P \\ I=\$11,749.38-\$8904.56 \\ I=\$2,844.82 \end{gathered}[/tex]b) If the amount invested is compounded continuously, this means that
n = 1. Using the previous formula and replacing the value of "n" as 1 will give;
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ A=8904.56(1+\frac{0.04}{1})^{1(7)} \\ A=8904.56(1.04)^7 \\ A=8904.56(1.3159) \\ A=\$11,717.79 \end{gathered}[/tex]The future value when interest is compounded continuously is approximately $11,717.79
Get the interest if compounded continuously
[tex]\begin{gathered} A=P+I \\ I=A-P \\ I=11,717.79-8904.56 \\ I\approx\$2,813.23 \end{gathered}[/tex]Hence the interest on the amount invested if compounded continuously is $2,813.23
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