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Answer: 5.5% compounded semiannually
Concept:
The formula for compound interest is: [tex]A=P(1+\frac{r}{n})^{nt}[/tex]
**Note**: Don't focus too much on the variables, since it might vary in different textbooks or teachings.
Solve:
Given information
P = $5000
t = 5 years
r₁ = 5.5%
n₁ = 2 (semiannually)
r₂ = 5.25%
n₂ = 12 (monthly)
Given formula
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
Substitute values into the formula
[tex]A=5000(1+\frac{0.055}{2})^{2*5}[/tex]
Simplify values in the parenthesis by addition
[tex]A=5000(1.0275)^{2*5}[/tex]
Simplify the exponents by multiplication
[tex]A=5000(1.0275)^{10}[/tex]
Simplify by multiplication
[tex]A=6558.26[/tex] (round to the nearest hundredths)
Substitute values into the formula
[tex]A=5000(1+\frac{0.0525}{2})^{2*5}[/tex]
Simplify values in the parenthesis by addition
[tex]A=5000(1.02625)^{2*5}[/tex]
Simplify the exponents by multiplication
[tex]A=5000(1.02625)^{10}[/tex]
Simplify by multiplication
[tex]A=6478.91[/tex] (round to the nearest hundredths)
Since, $6558.26 > $6478.91
Therefore, 5.5% compounded semiannually yields the greater return
Hope this helps!! :)
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