Question

Suppose that you have $3,000 to invest. Which investment yields the greater return over a 10 year period: 7.33% compounded daily or 7.4% compounded quarterly?

Find the total amount of the investment after 10 years if $3,000 is invested at 7.33% compounded daily.
$(Round to the nearest cent as needed.)

Answer 1

Using the compounded interest formula

`A = P\left(1+(r)/(n)\right)^(n\cdot t)`

we can calculate the two options.

Option #1: 7.33% compounded daily

`A = 3000\left(1+(0.0733)/(365)\right)^(365\cdot 10)\approx 6243.49`

Option #2: 7.4% compounded quarterly

`A = 3000\left(1+(0.074)/(4)\right)^(4\cdot 10)\approx 6245.43`

As a related calculation, since the principal and the time frame is the same, you could just compare the growth factors, the
`\left(1+(r)/(n)\right)^(n)` piece of the formulas, which will indicate the effective growth rates:

Option #1: 7.33% compounded daily has an growth factor of

`\left(1+(0.0733)/(365)\right)^(365) \approx 1.07604538569`

This is an effective growth rate of about 7.60454% per year.

Option #2: 7.4% compounded daily has an effective rate of

`\left(1+(0.074)/(4)\right)^(4) \approx 1.07607894364`

This is an effective growth rate of about 7.60789% per year.

This second option has a slight higher effective annual rate, so again, the second option is better.

Answer 2

you would make more compounded quarterly.

Explanation:

3000
`(1 + (.0733)/(365)) ^(365(10))`

$6,243.49

3000
`(1 + (.074)/(4)) ^(4(10))`

$6,245.43