The amount of money $20,000 is loaned for a period of time 6 years 9 months along with the simple interest $14,200 charged. determine the simple interest rate of the loan.

A = P (1 + rt)

Where: A = Total Accrued Amount (principal + interest)

P = Principal Amount

I = Interest Amount

r = Rate of Interest per year in decimal; r = R/100

t = Time Period involved in months

From the question given,

A = $34, 200

P = $20,000

I = $14,200

r = ?

T = 6 years, 9 months = 81 months

Substituting the original equation for r:

r = (1/t) (A/P - 1)

Solving our equation:

r = (1/81) ((34200/20000) - 1) = 0.00876543

r = 0.00876543

Converting r decimal to R a percentage

R = 0.00876543 * 100 = 0.8765%/month

R = 0.8765% per month

Calculating the annual rate

0.8765%/month * 12 months/year = 10.518%/year.