Question

The new england trader earned 286.16 interest in 300 days from an investment that paid 7%. find the amount initially invested?

a) $2,000
b) $2,500
c) $3,000
d) $3,500

Answer 1

The initial amount invested that earned $286.16 interest over 300 days at a 7% interest rate is found to be $3,000 after rearranging and solving the simple interest formula.

Step-by-step explanation:

The question given asks us to find the initial amount invested given that the investment earned $286.16 of interest at a 7% interest rate over 300 days. To solve this, we need to rearrange the formula for calculating simple interest, I = Prt, where I is the interest earned, P is the principal amount (initial investment), r is the annual interest rate (as a decimal), and t is the time in years.

First, we convert the annual interest rate to a daily rate since the interest was earned over 300 days, and then convert those 300 days into a portion of a year. Since there are typically 365 days in a year, the time in years (t) is 300/365.

Using the formula I = Prt, and the given interest earned ($286.16), the time t as 300/365, and the annual interest rate r as 7% or 0.07, we have:

$286.16 = P * 0.07 * (300/365)

We then solve for P, which gives us the initial investment:

P = $286.16 / (0.07 * (300/365))

P = $3,000

Therefore, the initial amount invested was $3,000, which corresponds to option (c).