If a borrower can afford to make monthly principal and interest payments of 1000 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 this buyer can afford

The the largest loan this buyer can afford is 14,533.75.

Explanation:

This can be determined using the formula for calculating the present value of an ordinary annuity as follows:

Step 1: Calculations of the present value or the loan the buyer can afford for a 30 year loan at 5 1/2%

PV30 = P * ((1 - (1 / (1 + r))^n) / r) …………………………………. (1)

Where;

PV30 = Present value or the loan the buyer can afford for a 30 year loan at 5 1/2% =?

P = monthly payment = 1000

r = interest rate = 5 1/2% = 5.50% = 0.055

n = number of years = 30

Substitute the values into equation (1) to have:

PV30 = 1000 * ((1 - (1 / (1 + 0.055))^30) / 0.055)

PV30 = 1000 * 14.5337451711221

PV30 = 14,533.75

Step 2: Calculation of the present value or the loan the buyer can afford for a 20 year loan at 4 1/2%

PV20 = P * ((1 - (1 / (1 + r))^n) / r) …………………………………. (2)

Where;

PV30 = Present value or the loan the buyer can afford for a 20 year loan at 4 1/2% =?

P = monthly payment = 1000

r = interest rate = 4 1/2% = 4.50% = 0.045

n = number of years = 20

Substitute the values into equation (1) to have:

PV20 = 1000 * ((1 - (1 / (1 + 0.045))^20) / 0.045)

PV20 = 1000 * 13.0079364514537

PV20 = 13,007.94

Conclusion

Since 14,533.75 which is the present value or the loan the buyer can afford for a 30 year loan at 5 1/2% is greater than the 13,007.94 which is the present value or the loan the buyer can afford for a 20 year loan at 4 1/2%, it therefore implies that the the largest loan this buyer can afford is 14,533.75.

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