A vacation home has a mortgage of $190,000 for 25 years at an annual interest rate of 5%.
a) Find the monthly mortgage payment.
b) During a month when $433.18 of the monthly mortgage payment is principal, how much of the payment is interest?

Question

A vacation home has a mortgage of $190,000 for 25 years at an annual interest rate of 5%. 
a) Find the monthly mortgage payment.
b) During a month when $433.18 of the monthly mortgage payment is principal, how much of the payment is interest?

Quizplus · Accepted Answer

a) Using the formula for monthly mortgage payments:

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

where 
M = monthly mortgage payment 
P = mortgage amount = $190,000 
i = monthly interest rate = 5% / 12 = 0.00417 
n = number of months = 25 years * 12 months/year = 300 months

Plugging in the values, we get:

M = $190,000 [ 0.00417(1 + 0.00417)^300 ] / [ (1 + 0.00417)^300 – 1] 
M = $1,110.72

Therefore, the monthly mortgage payment is $1,110.72.

b) During a month when $433.18 of the monthly mortgage payment is principal, we can subtract this amount from the total monthly payment to find the interest portion.

Interest = Monthly payment – Principal

Interest = $1,110.72 – $433.18

Interest = $677.54

Therefore, the interest portion of the monthly payment in this scenario is $677.54.

A Vacation Home Has a Mortgage of $190,000 for 25