You invest 3400 into account earning simple intrest. The balance is 4624 after 8 years. What is rate of intrest?

4624 = 3400(1+i)^8

(1+i)^8 = 1.36 take the 8th root of both sides
1+i = 1.03918
i = .03918 or 3.9%

We use the formula:

M = P( 1 + i )^n

M is the final amount including the principal.

P is the principal amount.

i is the rate of interest per year.

n is the number of years invested.

M = 4624

P = 3400

n = 8 years

We seek i.

4624 = 3400(1 + i)^8

You do the rest.

To find the rate of interest, we need to use the formula for simple interest:

Simple Interest = Principal * Rate * Time

We are given the following information:
Principal (P) = $3400
Balance (A) = $4624
Time (T) = 8 years

First, let's calculate the simple interest:
Simple Interest = Balance - Principal
Simple Interest = $4624 - $3400
Simple Interest = $1224

Now, we can substitute the values into the formula to solve for the rate of interest:
Rate = Simple Interest / (Principal * Time)
Rate = $1224 / ($3400 * 8)
Rate ≈ 0.045 or 4.5% (rounded to two decimal places)

Therefore, the rate of interest is approximately 4.5%.