Respuesta :
This problem seems to be about simple interest rates, which is defined by the formula
[tex]P=\frac{a}{\frac{(1+r)^n-1}{r(1+r)^n}}=\frac{a\cdot r(1+r)^n}{(1+r)^n-1}[/tex]Where P refers to the payment per month, r refers to the interest rate (divided by the number of months per year), t is time in years, n is the number of periods per year.
This formula is about amortized loan payments.
According to the problem, the final amount is unknown, the principal is $50,000.00, the interest rate is 0.05 (5%) and the time is 20 years. So, we need to substitute each value in the formula to find the amount we'll pay after the interest
[tex]P=\frac{50000\cdot0.004166666(1+0.004166666)^{240}}{(1+0.004166666)^{240}-1}=329.98[/tex]This means we are gonna pay back $329.76 per month.
It's important to consider that the rate r is found by dividing the interest 0.05 and the total months per year which are 12
[tex]\frac{0.05}{12}=0.041666666666\ldots[/tex]As you can observe, this is an infinite decimal number, so we take many decimal numbers as we need to get 329.98.
