Best answer:
This problem involves a few steps. First you have to calculate the payment on the 30 year mortgage, the remaining balance at 10 years on the 30 year mortgage and the payment on the 15 year mortgage. The formula for a payment on a mortgage is:
p = rL(1 + r)^t/((1 + r)^t - 1)
Where:
r = monthly rate
L = Loan amount
t = length of the...
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Best answer:
This problem involves a few steps. First you have to calculate the payment on the 30 year mortgage, the remaining balance at 10 years on the 30 year mortgage and the payment on the 15 year mortgage. The formula for a payment on a mortgage is:
p = rL(1 + r)^t/((1 + r)^t - 1)
Where:
r = monthly rate
L = Loan amount
t = length of the loan
For the 30 year mortgage:
r = 0.007 ---> (.084/12)
L = $127,262.85 ( $149,721.00*.85 ---> Amount after 15% down)
t = 360 (30 years * 12 months/year)
The payment for the 30 year mortgage is $969.54.
Now you need to calculate the balance of this loan at 10 years. The balance, B, is given by the following eqaution:
B = L(1 + r)^t - p/r*((1 + r)^t - 1)
Where:
r = 0.007 ---> (.084/12)
L = $127,262.85 ( $149,721.00*.85 ---> Amount after 15% down)
t = 120 (10 years * 12 months/year)
p = $969.54 (as calculated previously)
After 10 years the balance of the loan is $112,539.90 and there are 240 payments left. So this person will have to make 240 payments of $969.54. This means this person will pay $232,688.72 (240 * $969.54) over the next 20 years, but only $112,539.90 is principal (the remaining amount owed). So that means that the difference of $232,688.72 and $112,539.90 is the amount of interest this person will pay over the next 20 years. The amount of interest they will pay is $120,148.81 ($232,688.72 - $112,539.90).
Now calculate the payment on a 15 year mortgage using the payment formula above and the following amounts:
L = $112,539.90 (the remaining balance on the mortgage after 10 years)
r = 0.0045 (.054/12)
t = 180 (15 years * 12 months/year)
You should get a payment of $913.58 for the 15 year loan. Again, the person will make 180 payments of $913.58 for a total of $164,445.09 (180 * $913.58). But only $112,539.90 of that amount is principal, the rest is interest. The total amount of interest paid on the 15 year mortgage is $51,905.19 ($164,445.09 - $112,539.90).
Now to calculate the interest savings, subtract the 2 interest amounts.
$120,148.81 - $51,905.19 = $68,243.62
This means that the person would save $68,243.62 by switching to the 15 year mortgage.