An investment is made at 77% interest for 1 year. It grows to ​$3509.60. How much was originally invested​ (the principal)?
77% interest???
Oh, my!! I'd be happy with 1% or 2%!!
To find the original amount invested (the principal), we can use the formula for calculating simple interest:
Simple Interest = (Principal * Interest Rate * Time)
Given that the interest rate is 77% and the time period is 1 year, we can rewrite the formula as:
Simple Interest = (Principal * 0.77 * 1)
We are also given that the investment grows to $3509.60, which includes the principal and the interest. Therefore, we can set up an equation:
Principal + Simple Interest = Final Amount
Principal + (Principal * 0.77 * 1) = $3509.60
Now we can solve for the principal.
Let's rearrange the equation to isolate the principal on one side:
Principal + (Principal * 0.77 * 1) = $3509.60
Simplifying the equation, we have:
Principal + 0.77 * Principal = $3509.60
Combining like terms, we get:
1.77 * Principal = $3509.60
Now, solve for Principal:
Principal = $3509.60 / 1.77
Calculating this gives us:
Principal ≈ $1980.68
Therefore, the original amount invested (the principal) was approximately $1980.68.