Final answer:
The monthly payment for a $16,250 personal loan at an APR of 11.9% over a 10-year period is approximately $227.53.
Step-by-step explanation:
To calculate the required monthly payment for a personal loan of $16,250 with an APR of 11.9% over a 10-year period, we can use the formula for the monthly payment (R) on an installment loan which is derived from the amortization formula:
Amortization Formula:
R = P * [i(1+i)^n] / [(1+i)^n - 1]
Where:
- P = principal amount (the initial amount of the loan)
- i = monthly interest rate (APR divided by 12 months)
- n = total number of payments (loan term in years multiplied by 12 months)
For this particular loan, the values are:
- P = $16,250
- APR = 11.9% which means i = 11.9% / 12 months = 0.9917% monthly
- n = 10 years * 12 months = 120 payments
Now plug these values into the formula:
R = 16250 * [0.009917(1+0.009917)^120] / [(1+0.009917)^120 - 1]
Calculating this we get:
R = 16250 * [(0.009917)(3.3007)] / [3.3007 - 1]
R = $227.53 (after rounding to the nearest cent)
Thus, the required monthly payment for the personal loan would be approximately $227.53.