Question

Suppose that you have $5,000 to invest. Which investment yields the greater return over a 10 year period: 7.74% compounded daily or 7.8% compounded quarterly? Find the total amount of the investment after 10 years if $5,000 is invested at 7.74% compounded daily. $ (Round to the nearest cent as needed.)​

Answer 1

We should invest in 7.74% compounded daily as it yields a higher return.

The total investment after 10 years is $10,841.22.

Explanation:

a.) at 7.74% compounded daily

`final = principal(1 + (i)/(m) )^(m * n) \\ = 5000(1 + (0.0774)/(365) )^(365 * 10) \\ = 10 \: 841.2235`

I assumed there are 365 days in a year.

b.) at 7.8% compounded quarterly

`final = principal(1 + (i)/(m)) ^(m * n) \\ = 5000 (1 + (.078)/(4) )^(4 * 10) \\ = 10 \: 762.2505`