The maturity value of a 4-month loan of $8,250 is $8,363.50. What is the annual simple interest rate (in percent) on this loan? (Round your answer to one decimal place.)
To find the annual simple interest rate, we can use the formula for simple interest:
Interest = Principal x Rate x Time
Given that the principal (P) is $8,250, the maturity value (A) is $8,363.50, and the time (T) is 4 months (which is 1/3 of a year), we can calculate the interest:
Interest = A - P
Interest = $8,363.50 - $8,250
Interest = $113.50
Now, we can plug in the values into the formula to find the rate:
$113.50 = $8,250 x Rate x (1/3)
Rate = $113.50 / ($8,250 x 1/3)
Rate = $113.50 / $2,750
Rate = 0.0413
Converting to a percentage:
Rate = 0.0413 x 100
Rate = 4.13%
Therefore, the annual simple interest rate on this loan is 4.1%.