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

Answer:

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

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

Step-by-step explanation:

a.) at 7.74% compounded daily

$final = principal(1 + \frac{i}{m} )^{m \times n} \\ = 5000(1 + \frac{0.0774}{365} )^{365 \times 10} \\ = 10 \: 841.2235$

I assumed there are 365 days in a year.

b.) at 7.8% compounded quarterly

$final = principal(1 + \frac{i}{m}) ^{m \times n} \\ = 5000 (1 + \frac{.078}{4} )^{4 \times 10} \\ = 10 \: 762.2505$