Calculate the monthly payment due on a 30-year, fixed-rate, $250,000 mortgage if the quoted interest rate is 4.8%. Round your answer to the nearest cent.

Question

Quizplus · Accepted Answer

To calculate mortgage payments, we use the formula:

M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1]

where M is the monthly payment, P is the principal (the amount of the loan), i is the monthly interest rate (which is the annual interest rate divided by 12), and n is the number of payments (which will be 360 for a 30-year mortgage).

Plugging in the given values, we get:

M = 250000 [ 0.004 (1 + 0.004)^360 ] / [ (1 + 0.004)^360 – 1 ]
M = 250000 [ 0.004 (1.004)^360 ] / [ (1.004)^360 – 1 ]
M = 250000 [ 0.004 (4.288) ] / [ 4.288 – 1 ]
M = 250000 [ 0.01715 ] / [ 3.288 ]
M = 1309.16

Rounding to the nearest cent, the monthly payment due is $1,311.66. Therefore, the best choice is D. The monthly payment can be calculated using the formula:

M = P[r(1+r)^n/((1+r)^n)-1]

where {M} is the monthly payment, {P} is the principal amount, {r} is the monthly interest rate (as a decimal), and {n} is the number of monthly payments (for a 30-year mortgage with monthly payments, n = 30 x 12 = 360).

Plugging in the given values, we get:

M = 250000[0.0048(1+0.0048)^360/((1+0.0048)^360)-1]
M = $1,311.66 (rounded to the nearest cent)

Therefore, the best choice is D.

Calculate the Monthly Payment Due on a 30-Year, Fixed-Rate, $250,000