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)
A) 10000*(1+.05)^10
B) 10000*(1+.05/4)^40
C) 10000*(1+.05/12)^120
D) 10000*(1+.05/365)^3650
D alt) 10000*e^(.05*10)
A= P(1+r/n)^n*t
for instance A=10000(1+0.05/1)^1*10
A= 10000(1.05)^10
a= 10000(1.628895)
A= 16288.95
To find the future value of an investment with different compounding periods, you can use the formula for compound interest:
Future Value = Principal * (1 + (interest rate / number of compounding periods)) ^ (number of compounding periods * number of years)
Let's break down the formulas for each compounding period:
A) Annually:
Future Value = 10000 * (1 + 0.05)^10
This is because interest is compounded once a year for 10 years, so the formula raises the base amount, $10,000, to the power of 10.
B) Quarterly:
Future Value = 10000 * (1 + (0.05 / 4))^40
Interest is compounded every quarter for 10 years, so the formula raises the base amount to the power of (4 compounding periods per year * 10 years = 40).
C) Monthly:
Future Value = 10000 * (1 + (0.05 / 12))^120
Interest is compounded every month for 10 years, so the formula raises the base amount to the power of (12 compounding periods per year * 10 years = 120).
D) Daily (365 days):
Future Value = 10000 * (1 + (0.05 / 365))^3650
Interest is compounded daily for 10 years, so the formula raises the base amount to the power of (365 compounding periods per year * 10 years = 3650).
Alternatively, for the given case, you can also use the formula using the exponential function:
D alt) Future Value = 10000 * e^(0.05 * 10)
The exponential function with the base 'e' and the exponent of (interest rate * number of years) can be used to calculate the future value. In this case, e represents Euler's number.
By using these formulas, you can find the future value of the investment for each compounding period.