Question

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?

Answer 1

Answer: 5.5% compounded semiannually

Concept:

The formula for compound interest is:
`A=P(1+(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+(r)/(n))^(nt)`

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

Substitute values into the formula

`A=5000(1+(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+(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