Question

In the past seven years, Kathy’s uncle has been paying her monthly allowance of $1,000 in arrear, directly deposited into Kathy’s bank account, with an interest rate of 6% p.a. compounded monthly. Today, Kathy decides to use the accumulated sum of the monthly allowances her uncle pays for a cash down payment to buy a house. Kathy is currently prepared to pay up to $1,500 at the end of each month for a 20-year mortgage, and her bank is currently charging 4% p.a. interest, compounded monthly. What is the maximum house price Kathy can afford?

a.$2,246,914
b.$370,795
c.$28,779
d.$351,607

Answer 1

Kathy can afford a house with a maximum price of $351,607.

To calculate the maximum house price Kathy can afford, we need to find the total amount of money she will have at the end of the accumulation period and then calculate the mortgage payments she can afford.

First, let's calculate the future value of Kathy's monthly allowances after 7 years with 6% interest compounded monthly:

1. Calculate the number of monthly compounding periods: 7 years * 12 months/year = 84 months
2. Apply the compound interest formula: FV = P * (1 + r/n)^(n*t), where P = $1,000, r = 6% = 0.06, n = 12, and t = 7 years
3. Plug in the values and calculate the future value: FV = $1,000 * (1 + 0.06/12)^(12*7) = $116,394.53

Now, let's calculate the maximum house price Kathy can afford based on her monthly mortgage payments of $1,500 for 20 years with 4% interest compounded monthly:

1. Calculate the number of monthly compounding periods: 20 years * 12 months/year = 240 months
2. Apply the mortgage payment formula: PMT = PV * r / (1 - (1 + r)^(-n)), where PMT = -$1,500, r = 4% = 0.04, and n = 20 years * 12 months/year = 240 months
3. Plug in the values and calculate the present value (maximum house price Kathy can afford): PV = PMT * (1 - (1 + r)^(-n)) / r = -$1,500 * (1 - (1 + 0.04)^(-240)) / 0.04 = $351,607

Therefore, the maximum house price Kathy can afford is $351,607.