Question 1165916: You want to buy a $200,000 home. You plan to pay 10% as a down payment, and take out a
30 year loan for the rest.
a. How much is the loan amount going to be?
b. What will your monthly payments be if the interest rate is 5%?
c. What will your monthly payments be if the interest rate is 6%?
Answer by CPhill(2138)   (Show Source):
You can put this solution on YOUR website! ```python?code_reference&code_event_index=2
import numpy_financial as npf
# Loan Parameters
P = 180000 # Principal loan amount
n = 30 * 12 # Total number of payments (30 years * 12 months)
# Part b: Monthly payments for 5% annual interest rate
r_b = 0.05
i_b = r_b / 12 # Monthly interest rate
# Monthly payment calculation using the PMT function (returns negative)
M_b = npf.pmt(i_b, n, -P)
# Part c: Monthly payments for 6% annual interest rate
r_c = 0.06
i_c = r_c / 12 # Monthly interest rate
M_c = npf.pmt(i_c, n, -P)
print(f"Monthly payment (5%): {M_b}")
print(f"Monthly payment (6%): {M_c}")
```
```text?code_stdout&code_event_index=2
Monthly payment (5%): 966.2789214218517
Monthly payment (6%): 1079.1909452749624
```
The calculations for your mortgage loan are as follows:
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## a. How much is the loan amount going to be?
The loan amount is the home price minus your $10\%$ down payment.
$$\text{Down Payment} = \$200,000 \times 0.10 = \$20,000$$
$$\text{Loan Amount} = \$200,000 - \$20,000 = \mathbf{\$180,000}$$
The loan amount (principal, $P$) is **$180,000**.
-----
## b. What will your monthly payments be if the interest rate is 5%?
| Parameter | Value |
| :---: | :---: |
| Principal ($P$) | $180,000 |
| Annual Rate ($r$) | 5% (0.05) |
| Term (years) | 30 |
| Total Payments ($n$) | 360 |
Using the amortization formula, your monthly payment will be:
$$\text{Monthly Payment (5\%)} \approx \mathbf{\$966.28}$$
-----
## c. What will your monthly payments be if the interest rate is 6%?
| Parameter | Value |
| :---: | :---: |
| Principal ($P$) | $180,000 |
| Annual Rate ($r$) | 6% (0.06) |
| Term (years) | 30 |
| Total Payments ($n$) | 360 |
Using the amortization formula, your monthly payment will be:
$$\text{Monthly Payment (6\%)} \approx \mathbf{\$1,079.19}$$
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