Questions: [1: [-1/2.5 Points] Your first number to use for your notes Calculate the return values for 8000 earning interest at 5 years (Round your answer to two decimal places.) DETAILS MY NOTES AUFBXQ411.2027 2: [-1/2.5 Points] If we invest 3000 at an interest rate of 6% compounded daily, how much will be in the account after 5 years? (Round your answer to two decimal places.) DETAILS MY NOTES AUFBXQ411.2069 3: [-1/2.5 Points] Calculate the present value of 8000 earning interest at 5% compounded annually. A = 8000 (Round your answer to two decimal places.) DETAILS MY NOTES AUFBXQ411.2023 4: [-1/2.5 Points] Calculate the present value of 4000 earning interest at 7% compounded annually. A = 4000 (Round your answer to two decimal places.) DETAILS MY NOTES AUFBXQ411.2021]

Solution Steps

1. Calculate the return values for $8000 earning interest at 5 years:

   • Use the formula for compound interest: \( A = P(1 + r/n)^{nt} \)
   • Here, \( P = 8000 \), \( r \) is the interest rate, \( n \) is the number of times interest is compounded per year, and \( t \) is the number of years.

2. If we invest $3000 at an interest rate of 6% compounded daily, how much will be in the account after 5 years:

   • Use the same compound interest formula.
   • Here, \( P = 3000 \), \( r = 0.06 \), \( n = 365 \) (since interest is compounded daily), and \( t = 5 \).

3. Calculate the present value of $8000 earning interest at 5% compounded annually:

   • Use the present value formula: \( PV = \frac{A}{(1 + r/n)^{nt}} \)
   • Here, \( A = 8000 \), \( r = 0.05 \), \( n = 1 \) (since interest is compounded annually), and \( t = 5 \).

Using the compound interest formula:

\[ A = P(1 + r/n)^{nt} \]

where:

• \( P = 8000 \)
• \( r = 0.05 \)
• \( n = 1 \)
• \( t = 5 \)

Substituting the values:

\[ A = 8000(1 + 0.05/1)^{1 \cdot 5} = 8000(1.05)^{5} \approx 10210.25 \]

Using the same compound interest formula:

\[ A = P(1 + r/n)^{nt} \]

where:

• \( P = 3000 \)
• \( r = 0.06 \)
• \( n = 365 \)
• \( t = 5 \)

Substituting the values:

\[ A = 3000(1 + 0.06/365)^{365 \cdot 5} \approx 4049.48 \]

Using the present value formula:

\[ PV = \frac{A}{(1 + r/n)^{nt}} \]

where:

• \( A = 8000 \)
• \( r = 0.05 \)
• \( n = 1 \)
• \( t = 5 \)

Substituting the values:

\[ PV = \frac{8000}{(1 + 0.05/1)^{1 \cdot 5}} = \frac{8000}{(1.05)^{5}} \approx 6268.21 \]

Final Answer