I need to find the equation for the following (compound interest):
number of years: 12
initial principal: 10000
annual interest rate: 0.03
additional investment each subsequent quarter: 500
The value in 12 years is 43074.4088874
To find the equation for compound interest, we need to use the formula:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment/loan, including interest
P = the principal investment amount (initial principal)
r = annual interest rate (as a decimal)
n = number of times that interest is compounded per year
t = number of years
In this case, we have:
P = $10,000
r = 0.03 (3% annual interest rate)
n = 4 (interest is compounded quarterly)
t = 12 (number of years)
We can then substitute these values into the formula and solve for A:
A = 10000(1 + 0.03/4)^(4*12)
A = 10000(1 + 0.0075)^(48)
A = 10000(1.0075)^(48)
A ≈ 10000 * 1.411402724
From the given information, we know that the value in 12 years is $43,074.4088874. Therefore, we can set up the equation:
43074.4088874 = 10000 * 1.411402724
To solve for the value of A (the future value), divide both sides of the equation by 10000:
43074.4088874 / 10000 = 1.411402724
A ≈ 4.30744088874
Therefore, the equation for compound interest is approximately:
A ≈ 4.30744088874 * P
Hence, the formula for calculating the future value of an investment with compound interest is A ≈ 4.30744088874P.