Question

You are considering purchasing your first home. The price is $160,000, and you have saved up a $10,000 down payment. If you can get a mortgage loan at 5.2%, what will be your monthly payment to repay this loan?

Answer 1

Using BA II plus texas instrument calculator,

PV=($10,000)

FV=$160,000

N=12(since monthly payments have to be calculated)

I/Y=5.2%/12=0.43% p.a compounded monthly

CPT-PMT=$12,162

Answer 2

Solution: Calculating Monthly Mortgage Payment

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Step 1: Determine Loan Amount

• Home price: $160,000

• Down payment: $10,000

$$\text{Loan amount} = 160,000 - 10,000 = 150,000$$

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Step 2: Define Variables

• Loan amount $(P)$ = $150,000

• Annual interest rate $(r)$ = 5.2% or 0.052

• Monthly interest rate $(r_m)$:

$$r_m = \frac{0.052}{12} = 0.00433$$

• Loan term $(n)$:

$$n = 30 \times 12 = 360 \, \text{months}$$

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Step 3: Use the Mortgage Payment Formula

The formula to calculate the monthly mortgage payment is:

$$M = \frac{P \times r_m \times (1 + r_m)^n}{(1 + r_m)^n - 1}$$

Where:

• $M$ is the monthly payment

• $P = 150,000$

• $r_m = 0.00433$

• $n = 360$

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Step 4: Substitute the Values and Calculate

$$M = \frac{150,000 \times 0.00433 \times (1 + 0.00433)^{360}}{(1 + 0.00433)^{360} - 1}$$

After performing the calculation:

$$M \approx 823.67$$

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Step 5: Final Answer

$$\text{The monthly payment to repay this loan will be approximately } \mathbf{\$823.67.}$$

Answer 3

To determine your monthly mortgage payment for a $160,000homewitha$10,000 down payment and a 5.2% interest rate, here's a breakdown:

1. Loan Amount:
   $160,000(homeprice)-$10,000 (down payment) = $150,000.

2. Interest Rate and Term:

• Annual interest rate: 5.2%

• Monthly interest rate: $\frac{5.2\mathrm{\%}}{12}\approx 0.4333\mathrm{\%}$ or 0.004333 in decimal.

• Assumed loan term: 30 years (360 months).

3. Monthly Payment Formula:

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

   Where:

• $P=\mathrm{\$}150,000$ (loan amount)

• $r=0.004333$ (monthly interest rate)

• $n=360$ (number of payments).

4. Calculation:
   Plugging in the values, the monthly payment calculates to approximately:
   $823.08.

Final Answer:
Your monthly mortgage payment would be $823.08.