1.2k views
5 votes
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.)

User Uzbones
by
8.1k points

2 Answers

4 votes

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.

User Babanin
by
8.2k points
5 votes

Answer:

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

User RooiWillie
by
7.9k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories