Question

A family is purchasing a house and needs to finance a $195,000 mortgage from the bank with an annual percentage rate (APR) of 5.3%. The family is financing it over 30 vears and making monthly payments. What would their monthly payment be?​

Answer 1

Answer:

  a) payment: $1082.84

  b) interest: $194,822.40

Step-by-step explanation:

The monthly payment on the mortgage can be found using the given formula with the given values of principal (P=195000), interest rate (r=0.053), and time period (t=30). The value of n is 12, corresponding to the number of months in a year.

a)

The monthly payment is ...

  $k=\left(1+\dfrac{r}{n}\right)^{nt}=\left(1+\dfrac{0.053}{12}\right)^{12\cdot30}\approx 4.88661119\\\\\text{monthly payment}=\dfrac{P\cdot\dfrac{r}{n}\cdot k}{k-1}=\dfrac{195000\cdot0.0044166667\cdot4.88661119}{4.88661119-1}\\\\\boxed{\text{monthly payment}=\ 1082.84}$

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b)

The interest owed is the difference between the total of monthly payments and the principal of the loan:

  interest owed = (360)(1082.84) -195000 = 194,822.40

The interest owed over 30 years is $194,822.40.