You are thinking of purchasing a house the house costs 250000 you have 36000 in cash that you can use as a down payment on
the house but you need to borrow the rest of the purchase price the bank is offering a 30year mortgage that requires

Question

You are thinking of purchasing a house. The house costs $250,000. You have $36,000 in cash that you can use as a down payment on the house, but you need to borrow the rest of the purchase price. The bank is offering a 30-year mortgage that requires annual payments and has an interest rate of 9% per year. What will be your annual payment if you sign this mortgage? The annual payment is $____ (Round to the nearest dollar.)

baleno · Answer

To calculate the annual payment on a mortgage, we use the loan amortization formula:

A = P \cdot \frac{r(1 + r)^n}{(1 + r)^n - 1}

Where:

$A$ = annual payment (what we’re solving for)
$P$ = loan principal = cost of house − down payment = $250,000 - 36,000 = 214,000$
$r$ = annual interest rate = 9% = 0.09
$n$ = number of payments (30 years)

Step-by-step Calculation:

A = 214{,}000 \cdot \frac{0.09(1 + 0.09)^{30}}{(1 + 0.09)^{30} - 1}

First, compute $(1 + 0.09)^{30} = 1.09^{30} \approx 13.2687$

Then:

A = 214{,}000 \cdot \frac{0.09 \cdot 13.2687}{13.2687 - 1} = 214{,}000 \cdot \frac{1.1942}{12.2687}

A \approx 214{,}000 \cdot 0.09734 \approx 20{,}833

✅ Final Answer:

\boxed{\$20,833} \quad ext{(annual payment, rounded to the nearest dollar)}

Questions

You are thinking of purchasing a house the house costs 250000

Answers :

Step-by-step Calculation:

✅ Final Answer:

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