how to solve this problem:If a borrower can afford to make monthly principal and interest payments of $1,000 and the lender will make a 30-year loan at 5-1/2%, or a 20-year loan at 4-1/2%, what is the largest loan (rounded to the nearest $100) this buyer can afford?

30-year loan at 5-1/2% ⇒ MAXIMUM LOAN $176,100

using a loan amortization table, you will pay $5.6786 for every $1,000 that you borrow, so you can borrow up to $1,000 / $5.6786 = 176.1 thousands

principal = $176,100

first payment:

interests = $176,100 x 0.055 x 1/12 = $807.13

repaid principal = $192.87

20-year loan at 4-1/2% ⇒ MAXIMUM LOAN $158,000

using a loan amortization table, you will pay $6.3291 for every $1,000 that you borrow, so you can borrow up to $1,000 / $6.3291 = 158 thousands

principal = $158,000

first payment:

interests = $158,000 x 0.045 x 1/12 = $592.50

repaid principal = $407.50

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