how much did you invest if you earned $131.60 in interest at a rate of 4% for seven years?

I = PRT

131.6 = P * 0.04 * 4

To calculate the amount invested, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:
A = Total amount after interest (including initial investment)
P = Principal amount (initial investment)
r = Annual interest rate (as a decimal)
n = Number of times interest is compounded per year
t = Number of years

In this case, we have the following information:
Interest earned (A) = $131.60
Annual interest rate (r) = 4% = 0.04
Number of times compounded per year (n) = 1 (since it is not specified)
Number of years (t) = 7

Plugging in these values, we can solve for P:

$131.60 = P(1 + 0.04/1)^(1*7)

Simplifying,

1.04^7 * P = $131.60

Using a calculator, we find that 1.04^7 ≈ 1.3108.

1.3108 * P = $131.60

Now, we can solve for P:

P ≈ $131.60 / 1.3108

P ≈ $100

Therefore, the initial investment was approximately $100.

To find out how much you initially invested, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:
A = Final amount (including interest)
P = Principal amount (initial investment)
r = Annual interest rate (as a decimal)
n = Number of times the interest is compounded per year
t = Number of years

In this case, the final amount (A) is the principal amount (P) plus the interest earned, which is $131.60. The annual interest rate (r) is 4% or 0.04 as a decimal. The interest is compounded annually (n = 1), and the investment period is seven years (t = 7).

So, we can rewrite the formula as:

A = P(1 + 0.04/1)^(1*7)

Substituting in the values given:

131.60 = P(1 + 0.04)^7

Now we can solve for P:

P = 131.60 / (1 + 0.04)^7

Using a calculator, we can evaluate the equation:

P = 131.60 / (1.04)^7
P = 131.60 / 1.31224239
P ≈ $100

So, you initially invested approximately $100 to earn $131.60 in interest over seven years at an annual interest rate of 4%.