Bob buys a house for 150,000 with a mortgage rate of 5.8% convertible monthly. At the time of
purchase he owns a 10,000 20-year zero coupon bond that earns 4.5% annually. The bond
matures in 15 yeas. He would like to use the proceeds from the bond to make a payment larger
than the usual fixed rate payment and pay off the balance of the mortgage after the 180th
payment. How much should his monthly payments be?
i need answer of the above question
To find out how much Bob's monthly payments should be, we can use the mortgage formula to calculate the monthly payment amount. The formula is:
P = (r * PV) / (1 - (1 + r)^(-n))
Where:
P = Monthly payment amount
r = Monthly interest rate (annual interest rate / 12)
PV = Present value of the mortgage
n = Total number of payments
Let's break down the information given in the question:
Mortgage details:
- Mortgage amount: $150,000
- Mortgage rate: 5.8% convertible monthly
Bond details:
- Bond amount: $10,000
- Bond yield: 4.5% annually
- Bond maturity: 15 years
Given that the bond matures in 15 years and Bob wants to make the payment after the 180th payment, we need to calculate the total number of mortgage payments. Let's do that:
Total number of mortgage payments = 15 years * 12 months/year = 180 months
Now, let's calculate the present value (PV) of the mortgage:
PV = Mortgage amount - Bond amount = $150,000 - $10,000 = $140,000
Next, we'll calculate the monthly interest rate (r):
Monthly interest rate = Annual interest rate / 12 = 5.8% / 12 = 0.4833%
Using the formula mentioned earlier, we can now calculate the monthly payment amount (P):
P = (r * PV) / (1 - (1 + r)^(-n))
Substituting the values:
P = (0.4833% * $140,000) / (1 - (1 + 0.4833%)^(-180))
Now, we can solve this equation to find the monthly payment amount.