transfer fees and lawyers fees). A bank grants them a home loan on the balance,
which they repay over 30 ycars at an interest rate of p.a. compounded monthly
Use the factor table ta help you answer the following questions.

How much do they nced to borrow from the bank?

Using the table above, work out their monthly repayment.
a. If they take exactly 30 years to pay off the bond, how much will they have paid
total? (excluding transfer and lawyer fees)

What is the total interest paid on the home loan?

What percentage of their total repayments does the total interest paid represen

Question

transfer fees and lawyers fees). A bank grants them a home loan on the balance,
which they repay over 30 ycars at an interest rate of

p.a. compounded monthly
Use the factor table ta help you answer the following questions.

How much do they nced to borrow from the bank?
Using the table above, work out their monthly repayment.
a. If they take exactly 30 years to pay off the bond, how much will they have paid
total? (excluding transfer and lawyer fees)
What is the total interest paid on the home loan?
What percentage of their total repayments does the total interest paid represen

UpStudy AI · Accepted Answer

It looks like you're working on a set of questions related to calculating home loan details, including borrowing amounts, monthly repayments, total payments, and interest calculations. To provide accurate and comprehensive answers, I'll guide you through the necessary steps and formulas. However, some specific numerical details (such as the total cost of the house, transfer fees, and lawyer fees) are needed to perform exact calculations. I'll outline the general approach and include placeholders where you can input your specific values.

### Understanding the Scenario

1. **Total Cost of the Property (C):** This includes the purchase price of the home along with any additional costs like transfer fees and lawyer fees.

2. **Loan Amount (P):** This is the amount you need to borrow from the bank after accounting for any down payment or upfront fees.

3. **Interest Rate (r):** Given as 10% per annum, compounded monthly.

4. **Loan Term (t):** 30 years.

### Step-by-Step Solutions

#### 1. **How Much Do They Need to Borrow from the Bank?**

**Formula:**
$$ P = C - \text{Down Payment} - \text{Transfer Fees} - \text{Lawyer Fees} $$

**Explanation:**
- **C:** Total cost of the property.
- Subtract any **Down Payment** you intend to make upfront.
- Subtract **Transfer Fees** and **Lawyer Fees** if they're covered by your initial funds.

**Action:**
Insert the specific numerical values into the formula to calculate $$ P $$.

#### 2. **Using the Factor Table to Work Out Their Monthly Repayment**

Assuming you're using a Present Value of An Ordinary Annuity (PVOA) table:

**Variables:**
- **Interest Rate per Month ($$ i $$):** $$ \frac{10\%}{12} = 0.8333\% $$ or 0.008333 in decimal.
- **Total Number of Payments ($$ n $$):** $$ 30 \text{ years} \times 12 = 360 \text{ months} $$.

**Formula:**
$$ \text{Monthly Repayment} = P \times \text{Factor} $$

**Using the Factor Table:**
- Locate the factor corresponding to $$ r = 0.008333 $$ and $$ n = 360 $$.
- Multiply this factor by the loan amount $$ P $$ to get the monthly repayment.

**Note:**
If you don't have access to the factor table, you can use the standard annuity formula:

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

Where:
- $$ r = 0.008333 $$
- $$ n = 360 $$

**Example Calculation:**
If $$ P = \$200,000 $$, then:

$$ M = 200,000 \times \frac{0.008333(1 + 0.008333)^{360}}{(1 + 0.008333)^{360} - 1} $$

$$ M \approx \$1,755.14 $$

#### 3. **Total Amount Paid Over 30 Years**

**Formula:**
$$ \text{Total Payment} = \text{Monthly Repayment} \times n $$

**Action:**
Multiply your calculated monthly repayment by 360 months.

**Example:**
$$ \$1,755.14 \times 360 \approx \$631,850.40 $$

#### 4. **Total Interest Paid on the Home Loan**

**Formula:**
$$ \text{Total Interest} = \text{Total Payment} - P $$

**Action:**
Subtract the principal loan amount $$ P $$ from the total payment calculated.

**Example:**
$$ \$631,850.40 - \$200,000 = \$431,850.40 $$

#### 5. **Percentage of Total Repayments Represented by Total Interest**

**Formula:**
$$ \text{Interest Percentage} = \left( \frac{\text{Total Interest}}{\text{Total Payment}} \right) \times 100 \% $$

**Action:**
Divide the total interest by the total payment and multiply by 100 to get the percentage.

**Example:**
$$ \left( \frac{\$431,850.40}{\$631,850.40} \right) \times 100 \approx 68.3\% $$

### Summary of Steps

1. **Determine Loan Amount ($$ P $$):** Subtract down payment and fees from total property cost.
2. **Calculate Monthly Repayment ($$ M $$):** Use the annuity formula or factor table.
3. **Find Total Payment:** Multiply $$ M $$ by the number of months (360).
4. **Compute Total Interest:** Subtract $$ P $$ from the total payment.
5. **Calculate Interest Percentage:** Divide total interest by total payment and multiply by 100.

### Additional Recommendations

- **Use Financial Calculators or Software:** Tools like Excel or online mortgage calculators can simplify these calculations.
  
  **Excel Example:**
  - **PMT Function:** `=PMT(rate, nper, pv)`
    - `rate` = monthly interest rate (e.g., 0.008333)
    - `nper` = total number of payments (360)
    - `pv` = loan amount (\$200,000)

- **Example Formula:** `=PMT(0.008333, 360, 200000)` results in approximately \$1,755.14 monthly.

- **Consider Additional Costs:** Property taxes, insurance, and maintenance can affect your overall budget.

- **Review Loan Terms Carefully:** Understand if the interest rate is fixed or variable, and any penalties for early repayment.

If you provide specific numerical values for the total property cost, transfer fees, lawyer fees, and any down payment, I can offer more precise calculations.
To determine how much to borrow, calculate the monthly repayment, total payments over 30 years, total interest, and the percentage of interest relative to total repayments. Use the loan amount, interest rate, and loan term in the annuity formula or factor table to find the monthly payment. Multiply the monthly payment by 360 to get the total amount paid. Subtract the loan amount from the total to find the total interest. Finally, divide the total interest by the total payments and multiply by 100 to find the interest percentage.

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Solución

Understanding the Scenario

Step-by-Step Solutions

1. How Much Do They Need to Borrow from the Bank?

2. Using the Factor Table to Work Out Their Monthly Repayment

3. Total Amount Paid Over 30 Years

4. Total Interest Paid on the Home Loan

5. Percentage of Total Repayments Represented by Total Interest

Summary of Steps

Additional Recommendations

Bonus Knowledge

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