Answered

Explore Westonci.ca, the leading Q&A site where experts provide accurate and helpful answers to all your questions. Ask your questions and receive detailed answers from professionals with extensive experience in various fields. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.

If an account is increasing at a rate of [tex]\(2.1 \%\)[/tex] compounded monthly, what is the exact value of [tex]\(i\)[/tex] in the following future value ordinary annuity formula?

[tex]\[ F V = P \left( \frac{(1+i)^x - 1}{i} \right) \][/tex]

A. [tex]\(2.1\)[/tex]

B. [tex]\(\frac{0.021}{100}\)[/tex]

C. [tex]\(\frac{0.021}{12}\)[/tex]

D. [tex]\(\frac{0.21}{12}\)[/tex]

Sagot :

GinnyAnswer
To find the exact value of [tex]\( i \)[/tex] in the future value ordinary annuity formula:

[tex]\[ FV = P \left( \frac{(1+i)^x - 1}{i} \right) \][/tex]

we need to convert the given annual interest rate into a monthly interest rate, as the interest is compounded monthly.

Given:
- Annual interest rate ([tex]\( r \)[/tex]) = [tex]\( 2.1\% \)[/tex]

Step-by-step explanation:

1. Convert the annual interest rate to a decimal:

[tex]\[ r = \frac{2.1}{100} = 0.021 \][/tex]

2. Determine the monthly interest rate:

Since the interest rate is compounded monthly, we need to divide the annual rate by 12 (the number of months in a year):

[tex]\[ i = \frac{0.021}{12} \][/tex]

So the exact value of [tex]\( i \)[/tex] is:

[tex]\[ i = 0.00175 \][/tex]

Thus, the correct answer is:

c. [tex]\(\frac{0.021}{12}\)[/tex]
Visit us again for up-to-date and reliable answers. We're always ready to assist you with your informational needs. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Westonci.ca is your go-to source for reliable answers. Return soon for more expert insights.