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 ...
[tex]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}[/tex]
__
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.
