Mr. Hobbs was just about to take out a home mortage of $120,000 for 20 yrs at the rate of 10.0% compounded monthly. The monthly payments would have been $1158.03. But a competitive bank offered him a 30 yr mortgage at 9,5% which has monthly payments of $1009.03. Mr Gibbs went with the second bank because he assumed that a lower monthly payment and a lower interest rate would be a better bargain. Assuming that he could afford the higher payment; do you think he did the right thing? Explain your answer

Question

Mr. Hobbs was just about to take out a home mortage of $120,000 for 20 yrs at the rate of 10.0% compounded monthly. The monthly payments would have been $1158.03. But a competitive bank offered him a 30 yr mortgage at 9,5% which has monthly payments of $1009.03. Mr Gibbs went with the second bank because he assumed that a lower monthly payment and a lower interest rate would be a better bargain. Assuming that he could afford the higher payment; do you think he did the right thing? Explain your answer

Answer 1

Did you check if your previous post of the same question was answered?

Answer 2

why would the advantage me to go with lower interest rate?

Answer 3

To determine if Mr. Hobbs made the right decision in choosing the 30-year mortgage with a lower monthly payment and interest rate, let's compare the total cost of each mortgage over their respective terms.

First, let's calculate the total cost of the 20-year mortgage. The principal amount is $120,000. The interest rate is 10% compounded monthly, and the monthly payment is $1,158.03.

To calculate the total cost, we'll need to calculate the number of payments made over 20 years. Since the interest is compounded monthly, we have 20 * 12 = 240 payments.

Using the formula for the loan balance after t payments:
Loan balance = Principal * [(1 + (interest rate / 12))^(number of payments)] - [(monthly payment / interest rate) * ((1 + (interest rate / 12))^(number of payments) - 1)]

Let's substitute the given values into the formula:
Loan balance = 120000 * [(1 + (0.1 / 12))^(240)] - [(1158.03 / 0.1) * ((1 + (0.1 / 12))^(240) - 1)]

Solving this equation, we find that the total cost for the 20-year mortgage is approximately $277,191.47.

Now, let's calculate the total cost of the 30-year mortgage. The principal amount is still $120,000. The interest rate is 9.5%, compounded monthly, and the monthly payment is $1,009.03.

Using the same formula as above, we'll calculate the number of payments made over 30 years: 30 * 12 = 360 payments.

Substituting the values into the formula:
Loan balance = 120000 * [(1 + (0.095 / 12))^(360)] - [(1009.03 / 0.095) * ((1 + (0.095 / 12))^(360) - 1)]

Solving this equation, we find that the total cost for the 30-year mortgage is approximately $363,374.31.

By comparing the total cost, we can see that the 20-year mortgage has a lower total cost compared to the 30-year mortgage. Therefore, if Mr. Hobbs can afford the higher monthly payment, choosing the 20-year mortgage would be a better financial decision.

Even though the monthly payment and interest rate are lower for the 30-year mortgage, the longer term increases the total interest paid over the life of the loan. Overall, Mr. Hobbs would be paying less in total by choosing the 20-year mortgage.

It's important to note that this analysis assumes all other factors are equal and doesn't consider other potential financial goals or circumstances that Mr. Hobbs may have. It's always a good idea to evaluate your specific financial situation and consult with a financial advisor before making any mortgage decisions.