Question 1173889
Let's break down this mortgage calculation problem step-by-step.

**Q1: Monthly Payment for a $450,000 Loan (25 years, 4.25%)**

* **Loan Amount (P):** $450,000
* **Annual Interest Rate (r):** 4.25% or 0.0425
* **Monthly Interest Rate (i):** 0.0425 / 12 ≈ 0.00354167
* **Number of Payments (n):** 25 years * 12 months/year = 300 months

We'll use the mortgage payment formula:

M = P [ i(1 + i)^n ] / [ (1 + i)^n  -  1]

Where:

* M = Monthly payment
* P = Principal loan amount
* i = Monthly interest rate
* n = Total number of payments

Let's calculate:

M = 450000 [ 0.00354167(1 + 0.00354167)^300 ] / [ (1 + 0.00354167)^300  -  1]

M = 450000 [ 0.00354167(2.871036) ] / [ 2.871036  -  1 ]

M = 450000 [ 0.010196 ] / [ 1.871036 ]

M = 450000 * 0.00545

M ≈ $2,452.50

Therefore, Aya and Harumi would have to afford to pay approximately **$2,452.50** each month.

**Q2: Total Amount Paid to the Lender**

* Total Paid = Monthly Payment * Number of Payments
* Total Paid = $2,452.50 * 300
* Total Paid = $735,750

The total amount paid to the lender would be **$735,750**.

**Q3: Maximum Mortgage Amount with $2,000 Monthly Payment**

* **Monthly Payment (M):** $2,000
* **Monthly Interest Rate (i):** 0.00354167
* **Number of Payments (n):** 300

We'll rearrange the mortgage payment formula to solve for P:

P = M [ (1 + i)^n  -  1 ] / [ i(1 + i)^n ]

P = 2000 [ (1 + 0.00354167)^300  -  1 ] / [ 0.00354167(1 + 0.00354167)^300 ]

P = 2000 [ 1.871036 ] / [ 0.010196 ]

P = 2000 * 183.506

P ≈ $367,012

The maximum mortgage amount they could afford to borrow would be approximately **$367,012**.

**Q4: Total Amount Paid to the Lender (with $2,000 Payment)**

* Total Paid = Monthly Payment * Number of Payments
* Total Paid = $2,000 * 300
* Total Paid = $600,000

The total amount paid to the lender would be **$600,000**.