troy juth wants to purchase new dive equipment for underwater connection, his retail store in colorado springs. he was offered a $58,000 loan at 4% for 72 months. what is his monthly payment by formula?
To calculate the monthly payment, we can use the formula for the monthly payment on a loan:
\[ M = P \times \frac{r(1+r)^n}{(1+r)^n - 1} \]
Where:
M = monthly payment
P = principal loan amount
r = monthly interest rate
n = number of months
Given:
P = $58,000
r = 4% = 0.04 (monthly interest rate)
n = 72 (number of months)
Now, we can substitute the values into the formula:
\[ M = 58000 \times \frac{0.04(1+0.04)^{72}}{(1+0.04)^{72} - 1} \]
Simplifying further,
\[ M = 58000 \times \frac{0.04(1.04)^{72}}{(1.04)^{72} - 1} \]
Calculating the numerator and denominator separately:
Numerator = 0.04(1.04)^72 = 0.04(1.72) = 0.0688
Denominator = (1.04)^72 - 1 = 2.208 - 1 = 1.208
Substituting back into the formula:
\[ M = 58000 \times \frac{0.0688}{1.208} \]
Finally, calculating the monthly payment:
M = $3,292.053
Therefore, Troy Juth's monthly payment for the $58,000 loan at 4% for 72 months is approximately $3,292.05.