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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]
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