Mathematics

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?

2 Answer

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

    [tex]\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][/tex]
  • Answer:

    $ 568.74 ( approx )

    Step-by-step explanation:

    Since, the monthly payment formula is,

    [tex]P=\frac{PV(r)}{1-(1+r)^{-n}}[/tex]

    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

    [tex]=89900-\frac{20\times 89900}{100}[/tex]

    [tex]=89900-17980[/tex]

    [tex]=\$71920[/tex]

    APR = 5% = 0.05 ⇒ r = [tex]\frac{0.05}{12}[/tex] ( 1 year = 12 months ),

    Time = 15 years ⇒ n = 15 × 12 = 180

    Hence, the monthly payment would be,

    [tex]P=\frac{71920(\frac{0.05}{12})}{1-(1+\frac{0.05}{12})^{-180}}[/tex]

    [tex]=568.738776353[/tex]

    [tex]\approx \$ 568.74[/tex]

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