what formulas do i use for this:

Investments Suppose $10,000 is invested at an annual rate of 5% for 10 years. Find the future value if interest is compounded as follows.

A) Annually
B) Quarterly
C) Monthly
D)Daily (365 days)

In each case, use the formula
Future value = Initial value)*(1 + i)^n
where i is the interest fraction paid for the interval (year, quarter, month or day) and n is the number of intervals.
In case A), i = 0.05 and n = 10
In case B), i = 0.0125 and n = 40
Do the numbers. That's how you learn this stuff.

To calculate the future value of an investment with different compounding frequencies, we can use the formula:

Future value = Initial value * (1 + i)^n

Where:
- Initial value is the amount you initially invest ($10,000 in this case)
- i is the interest fraction paid for the compounding interval
- n is the number of compounding intervals

Now let's calculate the future value for each compounding frequency:

A) Annually:
For annual compounding, i = 0.05 (5% annual rate divided by 1 since it compounds once a year) and n = 10 (10 years).
Plugging these values into the formula:
Future value = $10,000 * (1 + 0.05)^10 = $16,289.47

B) Quarterly:
For quarterly compounding, i = 0.05/4 = 0.0125 (5% annual rate divided by 4 quarters in a year) and n = 10 * 4 = 40 (10 years multiplied by 4 quarters).
Plugging these values into the formula:
Future value = $10,000 * (1 + 0.0125)^40 = $16,374.46

C) Monthly:
For monthly compounding, i = 0.05/12 ≈ 0.004167 (5% annual rate divided by 12 months in a year) and n = 10 * 12 = 120 (10 years multiplied by 12 months).
Plugging these values into the formula:
Future value = $10,000 * (1 + 0.004167)^120 = $16,428.43

D) Daily (365 days):
For daily compounding, i = 0.05/365 ≈ 0.00013699 (5% annual rate divided by 365 days in a year) and n = 10 * 365 = 3,650 (10 years multiplied by 365 days).
Plugging these values into the formula:
Future value = $10,000 * (1 + 0.00013699)^3650 = $16,439.65

These calculations show how the frequency of compounding affects the future value of an investment. The more frequently compounding occurs, the higher the future value will be.