Question

Jamie purchased a condo for $89,900 with a down payment of 20%; her credit terms were 5% for 15 years. what is jamie's monthly payment?

Answer 1

$\bf \qquad \qquad \textit{Amortized Loan Value} \\\\ pymt=P\left[ \cfrac{\frac{r}{n}}{1-\left( 1+ \frac{r}{n}\right)^{-nt}} \right]$

$\bf \begin{cases} P= \begin{array}{llll} \textit{original amount}\\ \end{array}\to & \begin{array}{llll} \quad89900\\ \ \ -20\%\\ -17980\\ -----\\ \quad 71920 \end{array}\\ pymt=\textit{periodic payments}\\ r=rate\to 5\%\to \frac{5}{100}\to &0.05\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{payments are monthly, thus} \end{array}\to &12\\ t=years\to &15 \end{cases} \\\\\\ pymt=71920\left[ \cfrac{\frac{0.05}{12}}{1-\left( 1+ \frac{0.05}{12}\right)^{-12\cdot 15}} \right]$

Answer 2

Answer:

$ 568.74 ( approx )

Step-by-step explanation:

Since, the monthly payment formula is,

$P=\frac{PV(r)}{1-(1+r)^{-n}}$

Where,

PV = present value of the loan or borrowed amount,

r = monthly rate,

n = number of months,

Given,

The value of condo = $ 89,900,

Down payment rate = 20%,

Thus, the borrowed amount, PV = 89900 - 20% of 89900

$=89900-\frac{20\times 89900}{100}$

$=89900-17980$

$=\ 71920$

APR = 5% = 0.05 ⇒ r = $\frac{0.05}{12}$ ( 1 year = 12 months ),

Time = 15 years ⇒ n = 15 × 12 = 180

Hence, the monthly payment would be,

$P=\frac{71920(\frac{0.05}{12})}{1-(1+\frac{0.05}{12})^{-180}}$

$=568.738776353$

$\approx \ 568.74$