Answer:
Explanation:
The formula to calculate the monthly payment for a loan at a constant interest rate is:
[tex]P=L\times\frac{r(1+r)^n}{(1+r)^n-1}[/tex]
Where:
Then, further to the data provided, you need to knwo the loan amount and the interest rate per period.
I will compute the numbers assuming hypothetical numbers.
Assume L = 450,000 and r = 12%.
A) 15-year mortgage
[tex]P=450,000\times \frac{0.01(1+0.01)^{180}}{(1+0.01)^{180}-1}=$5,400.76[/tex]
That is the montly payment. Multiply by 180 to obtain the total amount paid and subtract the loan amount to obtain the total amount of interest paid over the life of the mortgage:
[tex]P\times 180 - \$ 450,000 = \$ 5,400.76\times 180-\$ 450,000=\$ 522,136.8[/tex]
B) 30-year mortgage
Substituting in the same formula:
[tex]P=450,000\times \frac{0.01(1+0.01)^{360}}{(1+0.01)^{360}-1}[/tex]
[tex]P=\$ 4,628.76[/tex]
Total payment: 360 × $4,628.76 = $1,666,353.60
Interests = $1,666,353.60 - $450,000 = $1,216,353.60
C) Difference
The difference is:
Based on the amount you will pay using both mortgages, the difference would see you pay c. $696,126.60 more.
Payment is monthly so you need to convert the interest and period to monthly basis. Loan amount is $650,000. APR is 9%.
Interest = 9% / 12 months
= 0.75%
Number of periods
15 years = 15 x 12 30 years = 30 x 12
= 180 months = 360 months
= Amount of Mortgage / Present value interest factor of annuity, 180 periods, 0.75%
= 650,000 / 98.59345
= $6,592.73 per month
= Amount of Mortgage / Present value interest factor of annuity, 360 periods, 0.75%
= 650,000 / 124.28179
= $5,230.05 per month
= Interest for 30 year mortgage - Interest for 15 year mortgage
= ( (Payment per month x 360 months) - Loan amount) - ( ( Payment per month x 180 months) - Loan amount)
= ( (5,230.05 x 360) - 650,000) - ( (6,592.73 x 180) - 650,000)
= $696,126.60
In conclusion, you would pay $696,126.60 more.
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