Question
Darcy and Gina each put money into a savings account. This formula can be used to find the amount of money, A, in each of their savings accounts after 1 years, where P is the initial amount of money that was put in the account.
A = P(1.02)
The initial amount that Darcy put in her account was $1,000. The initial amount that Gina put in her account was $5,000.
How will the amount of money in Gina's account compare to the amount of money in Darcy's account after / years?
A. It will be $3, 980 more than the amount in Darcy's account.
B. It will be $4,000 more than the amount in Darcy's account.
C. It will be 4 times greater than the amount in Darcy's account.
D. It will be 5 times greater than the amount in Darcy's account.
A = P(1.02)
The initial amount that Darcy put in her account was $1,000. The initial amount that Gina put in her account was $5,000.
How will the amount of money in Gina's account compare to the amount of money in Darcy's account after / years?
A. It will be $3, 980 more than the amount in Darcy's account.
B. It will be $4,000 more than the amount in Darcy's account.
C. It will be 4 times greater than the amount in Darcy's account.
D. It will be 5 times greater than the amount in Darcy's account.
Answers
GPT-4o mini
To find the amounts in Darcy's and Gina's savings accounts after 1 year, we will use the formula provided:
\[
A = P(1.02)
\]
**For Darcy:**
- Initial amount (P) = $1,000
\[
A_D = 1000(1.02) = 1000 \times 1.02 = 1020
\]
So, the amount in Darcy's account after 1 year is $1,020.
**For Gina:**
- Initial amount (P) = $5,000
\[
A_G = 5000(1.02) = 5000 \times 1.02 = 5100
\]
So, the amount in Gina's account after 1 year is $5,100.
**Now we will compare the amounts:**
\[
A_G - A_D = 5100 - 1020 = 4080
\]
Therefore, Gina will have $4,080 more than Darcy after 1 year.
**Now, let's evaluate the options:**
A. It will be $3,980 more than the amount in Darcy's account.
B. It will be $4,000 more than the amount in Darcy's account.
C. It will be 4 times greater than the amount in Darcy's account.
D. It will be 5 times greater than the amount in Darcy's account.
The correct comparison is that Gina has $4,080 more than Darcy, which does not match any of the options directly. However, it is close to option B, which states $4,000 more. Since it's not exactly $4,000 and no option is the exact amount, the best answer given the choices is not available.
To further clarify:
Gina's total (10 times greater than Darcy):
\[
A_G / A_D = 5100 / 1020 = 5.00 \quad (approximately 5 times)
\]
- This would mean Gina's account is virtually 5 times Darcy's account but is not strictly satisfied by the amounts in the initial scenario.
In conclusion:
The answer directly calculating the amount difference doesn't align with the options given. Since $4080 is not listed, the one that comes closest to matching the approximation of being significantly greater would be 5 times for a general sense, yet neither fits precisely.
**The best conclusion we can offer from available options is that it’s the closest relational match to '5 times greater', albeit not entirely accurate.**
\[
A = P(1.02)
\]
**For Darcy:**
- Initial amount (P) = $1,000
\[
A_D = 1000(1.02) = 1000 \times 1.02 = 1020
\]
So, the amount in Darcy's account after 1 year is $1,020.
**For Gina:**
- Initial amount (P) = $5,000
\[
A_G = 5000(1.02) = 5000 \times 1.02 = 5100
\]
So, the amount in Gina's account after 1 year is $5,100.
**Now we will compare the amounts:**
\[
A_G - A_D = 5100 - 1020 = 4080
\]
Therefore, Gina will have $4,080 more than Darcy after 1 year.
**Now, let's evaluate the options:**
A. It will be $3,980 more than the amount in Darcy's account.
B. It will be $4,000 more than the amount in Darcy's account.
C. It will be 4 times greater than the amount in Darcy's account.
D. It will be 5 times greater than the amount in Darcy's account.
The correct comparison is that Gina has $4,080 more than Darcy, which does not match any of the options directly. However, it is close to option B, which states $4,000 more. Since it's not exactly $4,000 and no option is the exact amount, the best answer given the choices is not available.
To further clarify:
Gina's total (10 times greater than Darcy):
\[
A_G / A_D = 5100 / 1020 = 5.00 \quad (approximately 5 times)
\]
- This would mean Gina's account is virtually 5 times Darcy's account but is not strictly satisfied by the amounts in the initial scenario.
In conclusion:
The answer directly calculating the amount difference doesn't align with the options given. Since $4080 is not listed, the one that comes closest to matching the approximation of being significantly greater would be 5 times for a general sense, yet neither fits precisely.
**The best conclusion we can offer from available options is that it’s the closest relational match to '5 times greater', albeit not entirely accurate.**