Answered

Find the best answers to your questions at Westonci.ca, where experts and enthusiasts provide accurate, reliable information. Join our platform to connect with experts ready to provide precise answers to your questions in various areas. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.

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]
We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.