Answer: 5.5% compounded semiannually
Concept:
The formula for compound interest is:
- 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)
<u>Given formula</u>
<h2>Find the compound interest for the first condition (5.5%)</h2>
<u>Substitute values into the formula</u>
<u>Simplify values in the parenthesis by addition</u>
<u>Simplify the exponents by multiplication</u>
<u>Simplify by multiplication</u>
(round to the nearest hundredths)
<h2>Find the compound interest for the second condition (5.25%)</h2>
<u>Substitute values into the formula</u>
<u>Simplify values in the parenthesis by addition</u>
<u>Simplify the exponents by multiplication</u>
<u>Simplify by multiplication</u>
(round to the nearest hundredths)
<h2>Compare the two conditions</h2>
Since, $6558.26 > $6478.91
Therefore, <u>5.5% compounded semiannually</u> yields the greater return
Hope this helps!! :)
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