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

a) payment: $1082.84

b) interest: $194,822.40

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+(r)/(n)\right)^(nt)=\left(1+(0.053)/(12)\right)^(12\cdot30)\approx 4.88661119\\\\\text{monthly payment}=(P\cdot(r)/(n)\cdot k)/(k-1)=(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.