WITH AN INVESTMENT AMOUNT OF $10,000 AND AN INTEREST RATE OF 5% OVER 15 YEARS, HOW MUCH PROFIT WILL YOU MAKE IF IT IS COMPOUNDED QUARTERLY? Between $9,000 and $10,500 Between $10,500 and $12,000 Between $12,500 and $14,000 More than $14,000WITH AN INVESTMENT AMOUNT OF $10,000 AND AN INTEREST RATE OF 5% OVER 15 YEARS, WHAT IS YOUR FINAL VALUE IF IT IS COMPOUNDED DAILY? Less than $14,000 Between $14,000 and $17,000 Between $17,000 and $20,000 More than $20,000WITH AN INVESTMENT AMOUNT OF $10,000 AND AN INTEREST RATE OF 5% OVER 15 YEARS, WHAT IS THE DIFFERENCE IN PROFIT BETWEEN THE DAILY COMPOUNDING AND YEARLY COMPOUNDING? No Difference Between $0 and $300 Between $300 and $500 More than $500WHICH SHOULD YOU CHOOSE AND WHY? OPTION 1: $1,000 WITH AN INTEREST RATE OF 20% OVER 10 YEARS OR OPTION 2: $1,000 WITH AN INTEREST RATE OF 8% OVER 25 YEARS. (WITH DAILY COMPOUNDING) 1 because the interest rate is higher 1 because the total return is the same for a shorter period of time 2 because the investment is over a longer period 1 or 2 because the total return is almost the sameWHICH COMPOUNDING SHOULD YOU CHOOSE GIVEN THE CHOICE OF YEARLY, AND DAILY AND WHY? Yearly because I only have to look once a year Daily because my return will be higher Daily because I can see my return every day Yearly because a year is longer than a day

Sure, let's break down each part of the question step by step.

Part 1: Compounded Quarterly

1. Investment Amount (P): $10,000
2. Annual Interest Rate (r): 5% or 0.05
3. Number of Years (t): 15
4. Compounding Frequency (n): Quarterly, so 4 times a year

The formula for compound interest is: $A = P \left(1 + \frac{r}{n}\right)^{nt}$

Plugging in the values: $A = 10000 \left(1 + \frac{0.05}{4}\right)^{4 \times 15}$ $A = 10000 \left(1 + 0.0125\right)^{60}$ $A = 10000 \left(1.0125\right)^{60}$

Using a calculator: $A \approx 10000 \times 2.1137$ $A \approx 21137$

The profit is: $\text{Profit} = A - P$ $\text{Profit} = 21137 - 10000$ $\text{Profit} = 11137$

So, the profit is between $10,500 and$12,000.

Part 2: Compounded Daily

1. Investment Amount (P): $10,000
2. Annual Interest Rate (r): 5% or 0.05
3. Number of Years (t): 15
4. Compounding Frequency (n): Daily, so 365 times a year

The formula for compound interest is: $A = P \left(1 + \frac{r}{n}\right)^{nt}$

Plugging in the values: $A = 10000 \left(1 + \frac{0.05}{365}\right)^{365 \times 15}$ $A = 10000 \left(1 + 0.000136986\right)^{5475}$ $A = 10000 \left(1.000136986\right)^{5475}$

Using a calculator: $A \approx 10000 \times 2.1170$ $A \approx 21170$

So, the final value is between $21,000 and$22,000.

Part 3: Difference in Profit Between Daily and Yearly Compounding

1. Yearly Compounding: $A = 10000 \left(1 + 0.05\right)^{15}$ $A = 10000 \left(1.05\right)^{15}$ $A \approx 10000 \times 2.0789$ $A \approx 20789$

Profit with yearly compounding: $\text{Profit} = 20789 - 10000$ $\text{Profit} = 10789$

Profit with daily compounding: $\text{Profit} = 21170 - 10000$ $\text{Profit} = 11170$

Difference in profit: $\text{Difference} = 11170 - 10789$ $\text{Difference} = 381$

So, the difference in profit is between $300 and$500.

Part 4: Choosing Between Two Investment Options

1. Option 1: $1,000 with an interest rate of 20% over 10 years $A = 1000 \left(1 + \frac{0.20}{365}\right)^{365 \times 10}$ $A \approx 1000 \times 7.388$ $A \approx 7388$

2. Option 2: $1,000 with an interest rate of 8% over 25 years $A = 1000 \left(1 + \frac{0.08}{365}\right)^{365 \times 25}$ $A \approx 1000 \times 7.322$ $A \approx 7322$

So, the total return is almost the same, but Option 1 gives a slightly higher return in a shorter period of time.

Part 5: Choosing Compounding Frequency

Daily compounding should be chosen because the return will be higher.