How do I solve this problem?

Question

Jay Jenkins takes out a 10.5% simple interest loan today that will be repaid 6 months from now with a payoff amount of $4000. What amount is Jay borrowing?

Answer 1

We know from the question that $40,000 = principal plus accrued interest over 6 months. It also tells us that the loan is for 6 months at an annual rate of 10.5%. Let's get started:

Let "x" denote the principal borrowed, aka the amount Jay is borrowing initially

0.105 * (6/12) x = 4,000 - x

0.0525 x = 4,000 - x

1.0525 x = 4,000

x = $3,800.48 (rounded)

Note:

1. Interest is calculated by taking half of the interest rate, because the specified state rate of 10.5% is assumed for over a year's time, as only 6 months elapsed, it is necessary to divide it in half