give answer in 2 step with explanation at the end of each step and final answer at the end:Cody and Carrie's goal is to purchase a home in the
future. They saw a house that would cost $820,000.
The

Question

give answer in 2 step with explanation at the end of each step and final answer at the end:Cody and Carrie's goal is to purchase a home in the
future. They saw a house that would cost $820,000.
The mortgage rate is 5.34% p.a., with a 25- year
amortization and a § - year term. Property taxes will be
$4,000 p.a. and heating would be $100 per month.
Property prices are forecasted to increase at a rate of
2.5% p.a. Carrie and Cody plan to save $1,000 a
month combined towards the down payment for 5
years (they are not doing this now). They will save the
money in their TFSA. They have come to you for advice
on whether this plan will save enough money for a
down payment. Cody and Carrie are also worried about
what would happen if one of them were to pass away.
They would want the other person to have enough
money to support themselves for 20 years. Carrie has
no life insurance, but Cody has life insurance equal to
1 -times his salary through work. The cost of this is $10
a month. They both have the option to buy disability
insurance as well but do not think t is worthwhile.
Carrie is considering the idea of creating an in - person
LLGP prep course. Based on the on the

VIPSolutions · Accepted Answer

## Step : Calculate the Future of the Home After 5 Years

- **Initial home value:** $820,000  
- **Annual property price increase:** 2.5%  
- **Number of years:** 5

We use the future value formula for compound growth:

$$
FV = PV \times (1 + r)^n
$$

Where:  
- $ PV = 820,000 $
- $ r = 2.5\% = .025 $
- $ n = 5 $

$$
FV = 820,000 \times (1 + .025)^5
$$
$$
FV = 820,000 \times (1.131408)
$$
$$
FV = 927,754.56
$$

**Explanation:**  
After 5 years, the home's value is projected to be **$927,755** (rounded to the nearest dollar).

---

## Step 2: Calculate the Remaining Mortgage Balance After 5 Years

- **Mortgage amount:** $820,000  
- **Mortgage rate:** 5.34% annual  
- **Amortization period:** 25 years  
- **Monthly payment calculation:**  
  - Number of monthly payments: 25 years × 12 = **300**
  - Monthly interest rate: 5.34% ÷ 12 = **.445%** (or .004450)

First, calculate the monthly mortgage payment ($ PMT $):

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

Where:  
- $ P = 820,000 $
- $ r = .004450 $
- $ n = 300 $

$$
PMT = 820,000 \times \frac{.004450(1+.004450)^{300}}{(1+.004450)^{300} - 1}
$$

Calculating $(1+.004450)^{300}$:

$$
(1+.004450)^{300} \approx 3.6825
$$

$$
PMT = 820,000 \times \frac{.004450 \times 3.6825}{3.6825 - 1}
$$
$$
PMT = 820,000 \times \frac{.016374}{2.6825}
$$
$$
PMT = 820,000 \times .006105
$$
$$
PMT \approx \$5,007
$$

Now, calculate the remaining mortgage after 5 years (60 payments):

The formula for the remaining balance after $ k $ payments:

$$
PV_{remaining} = PMT \times \frac{1 - (1 + r)^{-(n-k)}}{r}
$$
Where:  
- $ PMT = \$5,007 $
- $ r = .004450 $
- $ n-k = 300-60 = 240 $

$$
PV_{remaining} = 5,007 \times \frac{1 - (1 + .004450)^{-240}}{.004450}
$$
$$
(1 + .004450)^{-240} \approx .3363
$$
$$
PV_{remaining} = 5,007 \times \frac{1 - .3363}{.004450}
$$
$$
PV_{remaining} = 5,007 \times \frac{.6637}{.004450}
$$
$$
PV_{remaining} = 5,007 \times 149.2191
$$
$$
PV_{remaining} \approx \$747,063
$$

**Explanation:**  
After 5 years, the remaining mortgage balance will be **$747,063** (rounded to the nearest dollar).

---

## Final Answer: Amount of Equity After 5 Years

$$
\text{Equity} = \text{Future Home Value} - \text{Remaining Mortgage}
$$
$$
\text{Equity} = \$927,755 - \$747,063 = \$180,692
$$

---

### **Final Answer:**  
**Carrie and Cody will have approximately \$180,692 in equity in their property 5 years after purchase, assuming home values increase at 2.5% per year.**

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