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Question 7
2 pts
Suppose that you have $5000 to invest. Which investment yields the greater return over 5 years:
5.5% compounded semiannually or 5.25% compounded monthly?

Sagot :

eunice1234

Answer: 5.5% compounded semiannually

Concept:

The formula for compound interest is: [tex]A=P(1+\frac{r}{n})^{nt}[/tex]

  • A = Compound Interest
  • P = Principal Balance (or the amount of investment)
  • r = Interest Rate
  • n = The number of times interest is compounded
  • t = number of time periods given

**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]

Find the compound interest for the first condition (5.5%)

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)

Find the compound interest for the second condition (5.25%)

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)

Compare the two conditions

Since, $6558.26 > $6478.91

Therefore, 5.5% compounded semiannually yields the greater return

Hope this helps!! :)

Please let me know if you have any questions

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