We have to calculate the monthly payments (number of subperiods per year n = 12) for a loan of $14,000 (P = 14000) for five years (t = 5) at an interest rate of 6% (r = 0.06).
We can use the annuity formula to calculate the monthly payment (PMT) as:
[tex]\begin{gathered} \text{PMT}=\frac{P(\frac{r}{n})}{\lbrack1-(1+\frac{r}{n})^{-nt}\rbrack} \\ \text{PMT}=\frac{14000\cdot(\frac{0.06}{12})}{\lbrack1-(1+\frac{0.06}{12})^{-12\cdot5}\rbrack} \\ \text{PMT}=\frac{14000\cdot0.005}{\lbrack1-1.005^{-60}\rbrack} \\ \text{PMT}\approx\frac{14000\cdot0.005}{1-0.74137} \\ \text{PMT}\approx\frac{70}{0.25863} \\ \text{PMT}\approx270.66 \end{gathered}[/tex]
Answer: the monthly payments will be $270.66
