To calculate the monthly payment for a $14,790 auto loan over four years at 6.9% annual interest, we will use the given formula:
\[ P = \frac{A \times (r/n) \times (1 + (r/n))^{nt}}{(1 + (r/n))^{nt} - 1} \]
where:
- \( A \) = amount to finance = $14,790
- \( r \) = annual interest rate = 6.9% = 0.069
- \( n \) = number of times interest is compounded in one year = 12 (monthly)
- \( t \) = number of years = 4
First, we need to calculate \( r/n \):
\[ \frac{r}{n} = \frac{0.069}{12} \approx 0.00575 \]
Next, calculate \( nt \):
\[ nt = 12 \times 4 = 48 \]
Now, we calculate \( (1 + (r/n))^{nt} \):
\[ 1 + \frac{r}{n} = 1 + 0.00575 \approx 1.00575 \] \[ (1.00575)^{48} \approx 1.2987 \]
Now we can substitute everything into the formula for \( P \):
\[ P = \frac{14790 \times 0.00575 \times 1.2987}{1.2987 - 1} \]
Calculating the numerator:
\[ 14790 \times 0.00575 \times 1.2987 \approx 109.14185 \]
And the denominator:
\[ 1.2987 - 1 \approx 0.2987 \]
Now, calculate \( P \):
\[ P \approx \frac{109.14185}{0.2987} \approx 365.27 \]
Therefore, the monthly payment is approximately:
\[ P \approx 365.27 \]
Based on the choices given, it seems there's a mismatch with the calculated number. The closest amount that we can find from the original options would not perfectly match, but it’s essential to double-check the parameters and the operations if any clarifications or adjustments would yield your expected values.
However, based on the options presented, none of them are exactly matching the computed result from the formula application. Please revise any potential input or selection mistakes.
1 answer