Question

Question 7

Answer 1

Answer: 5.5% compounded semiannually

Concept:

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

• 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

$A=P(1+\frac{r}{n})^{nt}$

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

Substitute values into the formula

$A=5000(1+\frac{0.055}{2})^{2*5}$

Simplify values in the parenthesis by addition

$A=5000(1.0275)^{2*5}$

Simplify the exponents by multiplication

$A=5000(1.0275)^{10}$

Simplify by multiplication

$A=6558.26$ (round to the nearest hundredths)

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

Substitute values into the formula

$A=5000(1+\frac{0.0525}{2})^{2*5}$

Simplify values in the parenthesis by addition

$A=5000(1.02625)^{2*5}$

Simplify the exponents by multiplication

$A=5000(1.02625)^{10}$

Simplify by multiplication

$A=6478.91$ (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