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
check on payments for each
1)
120000 = pay[1 + 1.00833333^-240]/.0083333
payment = 1158.03
2) 120000 = pay [ 1+ 1.00791666^-360 ]/.00791666
payment = 1009.02
Since the second had a lower interest rates, it should be his choice.
The advantage will be with the lower rate.
To determine whether Mr. Hobbs made the right decision, we need to compare the total costs of both mortgage options over their respective terms. Let's calculate the total cost for each mortgage and analyze the results.
1. First, let's calculate the total cost for the original mortgage.
Total cost = monthly payment * number of payments
Monthly payment = $1158.03
Number of payments = 20 years * 12 months/year = 240 months
Total cost = $1158.03 * 240 = $277,927.20
2. Now, let's calculate the total cost for the second mortgage.
Total cost = monthly payment * number of payments
Monthly payment = $1009.03
Number of payments = 30 years * 12 months/year = 360 months
Total cost = $1009.03 * 360 = $362,650.80
Based on the calculations, we can see that the total cost of the second mortgage is higher than the total cost of the original mortgage. Therefore, choosing the second mortgage with the lower monthly payment and lower interest rate may not be the best financial decision.
While the lower monthly payment may seem more affordable, it stretches the repayment period from 20 to 30 years, resulting in a significantly higher total cost over time.
It is important to consider the long-term implications and total cost of a mortgage rather than solely focusing on the monthly payment. In this case, Mr. Hobbs could have saved approximately $84,723.60 by choosing the original mortgage.
Ultimately, the decision depends on Mr. Hobbs' financial goals, preferences, and ability to afford the higher payment. It is advisable to thoroughly consider the total cost, repayment period, and individual financial circumstances before making such decisions.