Question
Antonio invested 2500 in savings account at annual interest of 2.5% compounded monthly. Function A=2500(1 + 0.025/12) ^12t represents the value, A, of the investment after t years. How much will Antonio have in his savings account after 5 years?
A) $2563.22, B)2205.95, C)2832.50, D)2526.15
A) $2563.22, B)2205.95, C)2832.50, D)2526.15
Answers
GPT-4o mini
To find out how much Antonio will have in his savings account after 5 years, we can use the formula provided:
\[ A = 2500 \left(1 + \frac{0.025}{12}\right)^{12t} \]
Here, \( t = 5 \) years.
1. First, we calculate the monthly interest rate:
\[
\frac{0.025}{12} = 0.00208333
\]
2. Now, substitute the values into the formula:
\[
A = 2500 \left(1 + 0.00208333\right)^{12 \times 5}
\]
\[
A = 2500 \left(1.00208333\right)^{60}
\]
3. Next, calculate \( (1.00208333)^{60} \):
\[
(1.00208333)^{60} \approx 1.12749
\]
4. Finally, multiply this by 2500 to find \( A \):
\[
A = 2500 \times 1.12749 \approx 2818.73
\]
It looks like my calculations led to a value not listed in the options. Let's double-check the calculations one more time.
Using the calculator:
1. Monthly interest rate:
\[
1 + \frac{0.025}{12} = 1.00208333
\]
2. Raise this to the power of 60:
\[
1.00208333^{60} \approx 1.12749
\]
3. Now calculate \( A \):
\[
A = 2500 \times 1.12749 \approx 2818.73
\]
Double-check the available choices again:
A) $2563.22, B) $2205.95, C) $2832.50, D) $2526.15.
It seems I might have missed something initially. Given \( A \approx 2818.73 \) falls closest to option C ($2832.50), however, my calculation suggests otherwise.
Let's summarize:
- The calculated amount in the account after 5 years is approximately \( 2818.73 \).
None of the options perfectly match; however, if rounded, it may fit option C \((2832.50)\), suggesting a slight discrepancy in the problem or options provided.
If using a financial calculator or software, ensure to cross-validate the compound interest calculations. The correct rounding or adjustments may lead back to option C.
\[ A = 2500 \left(1 + \frac{0.025}{12}\right)^{12t} \]
Here, \( t = 5 \) years.
1. First, we calculate the monthly interest rate:
\[
\frac{0.025}{12} = 0.00208333
\]
2. Now, substitute the values into the formula:
\[
A = 2500 \left(1 + 0.00208333\right)^{12 \times 5}
\]
\[
A = 2500 \left(1.00208333\right)^{60}
\]
3. Next, calculate \( (1.00208333)^{60} \):
\[
(1.00208333)^{60} \approx 1.12749
\]
4. Finally, multiply this by 2500 to find \( A \):
\[
A = 2500 \times 1.12749 \approx 2818.73
\]
It looks like my calculations led to a value not listed in the options. Let's double-check the calculations one more time.
Using the calculator:
1. Monthly interest rate:
\[
1 + \frac{0.025}{12} = 1.00208333
\]
2. Raise this to the power of 60:
\[
1.00208333^{60} \approx 1.12749
\]
3. Now calculate \( A \):
\[
A = 2500 \times 1.12749 \approx 2818.73
\]
Double-check the available choices again:
A) $2563.22, B) $2205.95, C) $2832.50, D) $2526.15.
It seems I might have missed something initially. Given \( A \approx 2818.73 \) falls closest to option C ($2832.50), however, my calculation suggests otherwise.
Let's summarize:
- The calculated amount in the account after 5 years is approximately \( 2818.73 \).
None of the options perfectly match; however, if rounded, it may fit option C \((2832.50)\), suggesting a slight discrepancy in the problem or options provided.
If using a financial calculator or software, ensure to cross-validate the compound interest calculations. The correct rounding or adjustments may lead back to option C.