QuestionMay 24, 2025

Problem 9: Tuition will be approximately 25,000 in 6 years' time Money invested now will earn interest at 8% per year, compounded monthly The amount of money that should be invested now to have a value of 25,000 in 6 years' time is what? Show all solving steps needed before writing your answer in a complete sentence. Problem 10: You earned some money this summer and want to invest it so you can save for your next vacation. Put the banks in order of best earnings from highest to lowest. Bank A: Investments are compounded weekly with a 2% interest rate. 3ank B: Investments are compounded continuously with a 2% interest rate. ank C: Investments are compounded annually with a 2% interest rate.

Problem 9: Tuition will be approximately 25,000 in 6 years' time Money invested now will earn interest at 8% per year, compounded monthly The amount of money that should be invested now to have a value of 25,000 in 6 years' time is what? Show all solving steps needed before writing your answer in a complete sentence. Problem 10: You earned some money this summer and want to invest it so you can save for your next vacation. Put the banks in order of best earnings from highest to lowest. Bank A: Investments are compounded weekly with a 2% interest rate. 3ank B: Investments are compounded continuously with a 2% interest rate. ank C: Investments are compounded annually with a 2% interest rate.
Problem 9: Tuition will be approximately 25,000 in 6 years' time Money invested now will earn interest at 8% per year, compounded monthly The amount of money that should be invested now to have a value of 25,000 in 6 years' time is what? Show all solving steps needed before writing your answer in a complete sentence. Problem 10: You earned some money this summer and want to invest it so you can save for your next vacation. Put the banks in order of best earnings from highest to lowest. Bank A: Investments are compounded weekly with a 2% interest rate. 3ank B: Investments are compounded continuously with a 2% interest rate. ank C: Investments are compounded annually with a 2% interest rate.

Solution
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Answer

Problem 9: The amount of money needed now is approximately \15,625.25. ### Problem 10: Order of banks from best earnings to lowest: Bank B, Bank A, Bank C. Explanation 1. Calculate Present Value for Problem 9 Use the formula for compound interest: P = \frac{A}{(1 + \frac{r}{n})^{nt}}, where A = 25000, r = 0.08, n = 12, and t = 6. 2. Substitute Values into Formula for Problem 9 P = \frac{25000}{(1 + \frac{0.08}{12})^{12 \times 6}} 3. Compute Present Value for Problem 9 Calculate (1 + \frac{0.08}{12})^{72}, then divide 25000 by this result to find P. 4. Compare Banks for Problem 10 Calculate effective annual rates using formulas: - Bank A: r_{eff} = (1 + \frac{0.02}{52})^{52} - 1 - Bank B: r_{eff} = e^{0.02} - 1 - Bank C: r_{eff} = 0.02 5. Rank Banks for Problem 10 Compare calculated effective annual rates to rank banks from highest to lowest.

Explanation

1. Calculate Present Value for Problem 9<br /> Use the formula for compound interest: $P = \frac{A}{(1 + \frac{r}{n})^{nt}}$, where $A = 25000$, $r = 0.08$, $n = 12$, and $t = 6$.<br /><br />2. Substitute Values into Formula for Problem 9<br /> $P = \frac{25000}{(1 + \frac{0.08}{12})^{12 \times 6}}$<br /><br />3. Compute Present Value for Problem 9<br /> Calculate $(1 + \frac{0.08}{12})^{72}$, then divide $25000$ by this result to find $P$.<br /><br />4. Compare Banks for Problem 10<br /> Calculate effective annual rates using formulas:<br />- Bank A: $r_{eff} = (1 + \frac{0.02}{52})^{52} - 1$<br />- Bank B: $r_{eff} = e^{0.02} - 1$<br />- Bank C: $r_{eff} = 0.02$<br /><br />5. Rank Banks for Problem 10<br /> Compare calculated effective annual rates to rank banks from highest to lowest.
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