SOLUTION: You can afford a monthly mortgage payment of $1,650 and can get a 15-year 5.625% loan. What is the maximum loan you can get so your payment does not exceed $1,650?

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Question 1116952: You can afford a monthly mortgage payment of $1,650 and can get a 15-year 5.625% loan. What is the maximum loan you can get so your payment does not exceed $1,650?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

The formula to compute the monthly payment is
P+=+L%2A%28c%281%2Bc%29%5En%29%2F%28%281%2Bc%29%5En-1%29
where,
L = loan amount
P = monthly payment
c = interest rate per period
n = number of periods

In this case,
L = unknown
P = 1650
c = r/12 = 0.05625/12 = 0.0046875
n = 12*y = 12*15 = 180 months

Plug in the given info. Then solve for L
P+=+L%2A%28c%281%2Bc%29%5En%29%2F%28%281%2Bc%29%5En-1%29

1650+=+L%2A%280.0046875%281%2B0.0046875%29%5E180%29%2F%28%281%2B0.0046875%29%5E180-1%29

1650+=+L%2A%280.0046875%281.0046875%29%5E180%29%2F%28%281.0046875%29%5E180-1%29

1650+=+L%2A%280.0046875%2A2.32049057740442%29%2F%282.32049057740442-1%29

1650+=+L%2A%280.01087729958159%29%2F%281.32049057740442%29

1650+=+L%2A0.00823731707572

%281650%29%2F%280.00823731707572%29+=+%28L%2A0.00823731707572%29%2F%280.00823731707572%29

200307.938231912+=+L

L+=+200307.938231912
Round to the nearest dollar to get L = 200308. This is the max L can be so that P does not exceed 1650 If L = 200308, then P = 1650.

Final Answer: 200308 dollars