$500 principal earning 4% compounded quarterly, after 6 yr
i = .04/4 = .01
n = 4(6) = 24
amount = 500(1.01)^24 = ....
The answer is
634.86732426
To find the amount of money earned after 6 years with a $500 principal earning 4% compounded quarterly, you can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal amount
r = the interest rate (as a decimal)
n = the number of times interest is compounded per year
t = the number of years
In this case:
P = $500
r = 4% = 0.04 (as a decimal)
n = 4 (quarterly compounding)
t = 6 years
Plugging in the values, the formula becomes:
A = $500(1 + 0.04/4)^(4*6)
Simplifying:
A = $500(1 + 0.01)^(24)
A = $500(1.01)^24
Using a calculator:
A ≈ $608.75
Therefore, after 6 years, the amount earned will be approximately $608.75.
To calculate the amount earned on a $500 principal with a 4% interest rate compounded quarterly over a period of 6 years, you need to use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = principal amount ($500)
r = interest rate (4% or 0.04 as a decimal)
n = number of compounding periods per year (4, since it's compounded quarterly)
t = number of years (6)
Plugging in the values into the formula, we get:
A = $500(1 + 0.04/4)^(4*6)
A = $500(1 + 0.01)^24
A = $500(1.01)^24
Using a calculator, we can evaluate the expression (1.01)^24, which gives us approximately 1.297
Now we can calculate the final amount:
A = $500 * 1.297
A ≈ $648.50
Therefore, after 6 years, the principal of $500 will have earned approximately $148.50, resulting in a total amount of $648.50.