Question

question 6 of 11 (1 point) | question attempt 1 of 10
round your answers in (a)-(d) to two decimal places, if necessary.
use the formula below as needed.
m=\frac{pcdot\frac{r}{n}}{1-(1 + \frac{r}{n})^{-nt}}
part 1 of 4
(a) find the down - payment.
the down payment is $ 47500.00
alternate answer:
the down payment is $ 47,500.
part 2 of 4
(b) find the amount of the mortgage.
the amount of the mortgage is $ 202,500
part: 2 / 4
part 3 of 4
(c) find the

Explanation:

Step1: Identify given values

We know the down - payment and mortgage amount from previous parts. But we need to know the values of $P$ (loan amount, which is the mortgage amount), $r$ (annual interest rate), $n$ (number of payments per year), and $t$ (number of years) to use the formula $M=\frac{P\cdot\frac{r}{n}}{1-(1 + \frac{r}{n})^{-nt}}$ to find the monthly payment. Since these values are not given in the problem statement, we assume we are supposed to use the mortgage amount $P = 202500$ and need to be provided with $r$, $n$, and $t$. Let's assume a common scenario: annual interest rate $r=0.04$ (4%), number of payments per year $n = 12$ (monthly payments), and number of years $t=30$.

Step2: Substitute values into formula

First, calculate $(1+\frac{r}{n})^{-nt}=(1+\frac{0.04}{12})^{-12\times30}$.
Let $x=\frac{0.04}{12}\approx0.00333$. Then $(1 + x)^{-nt}=(1 + 0.00333)^{-360}$.
Using a calculator, $(1 + 0.00333)^{-360}\approx0.302$.
Next, calculate $P\cdot\frac{r}{n}=202500\times\frac{0.04}{12}=202500\times0.00333 = 675$.
Then $M=\frac{675}{1 - 0.302}=\frac{675}{0.698}\approx967.05$.

Answer:

The monthly payment is approximately $\$967.05$