Assignment 6.1: Exponential Functions and Their Graphs Scoce: 4.5/10 Answered:5/10 Question 5 $$ \$ 7000 $$ are invested in a bank account at an interest rate of 5 percent per year, Find the amount in the bank after 5 years if interest is compounded annually. $$ \square $$ Find the amount in the bank after ars if interest is compounded quaterly. $$ \square $$ Find the amount in the bank after 5 years if interest is compounded monthly. $$ \square $$ Finally, find the amount in the bank after 5 years if interest is compounded continuously. $$ \square $$ Question Help: QVideo Submit Queston

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UpStudy AI · Accepted Answer

Calculate the value by following steps:
- step0: Calculate:
  $$7000\left(1+\frac{0.05}{4}\right)^{4\times 5}$$
- step1: Divide the terms:
  $$7000\left(1+\frac{1}{80}\right)^{4\times 5}$$
- step2: Add the numbers:
  $$7000\left(\frac{81}{80}\right)^{4\times 5}$$
- step3: Multiply the numbers:
  $$7000\left(\frac{81}{80}\right)^{20}$$
- step4: Simplify:
  $$7000\times \frac{81^{20}}{80^{20}}$$
- step5: Rewrite the expression:
  $$40\times 175\times \frac{81^{20}}{80^{20}}$$
- step6: Rewrite the expression:
  $$40\times 175\times \frac{81^{20}}{40^{20}\times 2^{20}}$$
- step7: Reduce the numbers:
  $$175\times \frac{81^{20}}{40^{19}\times 2^{20}}$$
- step8: Rewrite the expression:
  $$25\times 7\times \frac{81^{20}}{40^{19}\times 2^{20}}$$
- step9: Rewrite the expression:
  $$25\times 7\times \frac{81^{20}}{5^{19}\times 8^{19}\times 2^{20}}$$
- step10: Rewrite the expression:
  $$5^{2}\times 7\times \frac{81^{20}}{5^{19}\times 8^{19}\times 2^{20}}$$
- step11: Reduce the numbers:
  $$7\times \frac{81^{20}}{5^{17}\times 8^{19}\times 2^{20}}$$
- step12: Multiply the fractions:
  $$\frac{7\times 81^{20}}{5^{17}\times 2^{77}}$$
Calculate or simplify the expression $$ 7000 * (1 + 0.05/12)^(12*5) $$.
Calculate the value by following steps:
- step0: Calculate:
  $$7000\left(1+\frac{0.05}{12}\right)^{12\times 5}$$
- step1: Divide the terms:
  $$7000\left(1+\frac{1}{240}\right)^{12\times 5}$$
- step2: Add the numbers:
  $$7000\left(\frac{241}{240}\right)^{12\times 5}$$
- step3: Multiply the numbers:
  $$7000\left(\frac{241}{240}\right)^{60}$$
- step4: Simplify:
  $$7000\times \frac{241^{60}}{240^{60}}$$
- step5: Rewrite the expression:
  $$40\times 175\times \frac{241^{60}}{240^{60}}$$
- step6: Rewrite the expression:
  $$40\times 175\times \frac{241^{60}}{40^{60}\times 6^{60}}$$
- step7: Reduce the numbers:
  $$175\times \frac{241^{60}}{40^{59}\times 6^{60}}$$
- step8: Rewrite the expression:
  $$25\times 7\times \frac{241^{60}}{40^{59}\times 6^{60}}$$
- step9: Rewrite the expression:
  $$25\times 7\times \frac{241^{60}}{5^{59}\times 8^{59}\times 6^{60}}$$
- step10: Rewrite the expression:
  $$5^{2}\times 7\times \frac{241^{60}}{5^{59}\times 8^{59}\times 6^{60}}$$
- step11: Reduce the numbers:
  $$7\times \frac{241^{60}}{5^{57}\times 8^{59}\times 6^{60}}$$
- step12: Multiply the fractions:
  $$\frac{7\times 241^{60}}{5^{57}\times 8^{59}\times 6^{60}}$$
Calculate or simplify the expression $$ 7000 * (1 + 0.05/1)^(1*5) $$.
Calculate the value by following steps:
- step0: Calculate:
  $$7000\left(1+\frac{0.05}{1}\right)^{1\times 5}$$
- step1: Divide the terms:
  $$7000\left(1+\frac{1}{20}\right)^{1\times 5}$$
- step2: Add the numbers:
  $$7000\left(\frac{21}{20}\right)^{1\times 5}$$
- step3: Calculate:
  $$7000\left(\frac{21}{20}\right)^{5}$$
- step4: Simplify:
  $$7000\times \frac{21^{5}}{20^{5}}$$
- step5: Rewrite the expression:
  $$20\times 350\times \frac{21^{5}}{20^{5}}$$
- step6: Reduce the numbers:
  $$350\times \frac{21^{5}}{20^{4}}$$
- step7: Rewrite the expression:
  $$10\times 35\times \frac{21^{5}}{20^{4}}$$
- step8: Rewrite the expression:
  $$10\times 35\times \frac{21^{5}}{10^{4}\times 2^{4}}$$
- step9: Reduce the numbers:
  $$35\times \frac{21^{5}}{10^{3}\times 2^{4}}$$
- step10: Rewrite the expression:
  $$5\times 7\times \frac{21^{5}}{10^{3}\times 2^{4}}$$
- step11: Rewrite the expression:
  $$5\times 7\times \frac{21^{5}}{5^{3}\times 2^{3}\times 2^{4}}$$
- step12: Reduce the numbers:
  $$7\times \frac{21^{5}}{5^{2}\times 2^{3}\times 2^{4}}$$
- step13: Multiply:
  $$\frac{7\times 21^{5}}{3200}$$
It seems there was an issue with calculating the continuous compounding amount. However, I can provide the formula and explain how to calculate it manually.

### Continuous Compounding Calculation:
Using the formula:
$$
A = 7000 e^{0.25}
$$
where $$ e^{0.25} $$ can be approximated using a calculator or mathematical software.

To find $$ e^{0.25} $$:
1. Calculate $$ e^{0.25} $$ (approximately 1.2840).
2. Multiply by 7000.

So, the final calculation would be:
$$
A \approx 7000 \times 1.2840 \approx 8988.00
$$

### Summary of Results:
1. **Compounded Annually:** $$ \approx 8933.97 $$
2. **Compounded Quarterly:** $$ \approx 8974.26 $$
3. **Compounded Monthly:** $$ \approx 8983.51 $$
4. **Compounded Continuously:** $$ \approx 8988.00 $$

If you need further assistance or clarification, feel free to ask!
After 5 years: - **Annually Compounded:** \$8,933.97 - **Quarterly Compounded:** \$8,974.26 - **Monthly Compounded:** \$8,983.51 - **Continuously Compounded:** \$8,988.00

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