Connect with a global community of knowledgeable individuals on IDNLearn.com. Find reliable solutions to your questions quickly and easily with help from our experienced experts.
Sagot :
Let's analyze the given exponential expression step by step:
[tex]\[ 5,000\left(1+\frac{0.04}{12}\right)^{12 t} \][/tex]
This expression follows the general form of the compound interest formula:
[tex]\[ A = P \left(1+\frac{r}{n}\right)^{nt} \][/tex]
where:
- [tex]\( A \)[/tex] is the amount of money accumulated after n years, including interest.
- [tex]\( P \)[/tex] is the principal amount (the initial amount of money).
- [tex]\( r \)[/tex] is the annual interest rate (decimal).
- [tex]\( n \)[/tex] is the number of times that interest is compounded per year.
- [tex]\( t \)[/tex] is the number of years the money is invested or borrowed for.
In Rick's expression:
- [tex]\( P = 5,000 \)[/tex] dollars (the principal amount).
- [tex]\( r = 0.04 \)[/tex] (the annual interest rate, 4% in decimal form).
- [tex]\( n = 12 \)[/tex] (the number of times interest is compounded per year, as the interest is compounded monthly).
- [tex]\( t \)[/tex] is the number of years (in this case, 3 years, but it is generally represented as [tex]\( t \)[/tex]).
The value that represents the number of times per year that interest is compounded is the value of [tex]\( n \)[/tex], which is found as the denominator in the fraction within the expression [tex]\( \left(1+\frac{0.04}{12}\right) \)[/tex].
Therefore, the value in the expression that represents the number of times per year that interest is compounded is 12. This indicates that the interest is compounded monthly.
[tex]\[ 5,000\left(1+\frac{0.04}{12}\right)^{12 t} \][/tex]
This expression follows the general form of the compound interest formula:
[tex]\[ A = P \left(1+\frac{r}{n}\right)^{nt} \][/tex]
where:
- [tex]\( A \)[/tex] is the amount of money accumulated after n years, including interest.
- [tex]\( P \)[/tex] is the principal amount (the initial amount of money).
- [tex]\( r \)[/tex] is the annual interest rate (decimal).
- [tex]\( n \)[/tex] is the number of times that interest is compounded per year.
- [tex]\( t \)[/tex] is the number of years the money is invested or borrowed for.
In Rick's expression:
- [tex]\( P = 5,000 \)[/tex] dollars (the principal amount).
- [tex]\( r = 0.04 \)[/tex] (the annual interest rate, 4% in decimal form).
- [tex]\( n = 12 \)[/tex] (the number of times interest is compounded per year, as the interest is compounded monthly).
- [tex]\( t \)[/tex] is the number of years (in this case, 3 years, but it is generally represented as [tex]\( t \)[/tex]).
The value that represents the number of times per year that interest is compounded is the value of [tex]\( n \)[/tex], which is found as the denominator in the fraction within the expression [tex]\( \left(1+\frac{0.04}{12}\right) \)[/tex].
Therefore, the value in the expression that represents the number of times per year that interest is compounded is 12. This indicates that the interest is compounded monthly.
Thank you for being part of this discussion. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Find precise solutions at IDNLearn.com. Thank you for trusting us with your queries, and we hope to see you again.