Question

You can afford a $1200 per month mortgage payment. You've found a 30 year loan at 7% interest.a) How big of a loan can you afford?$b) How much total money will you pay the loan company?c) How much of that money is interest?$

Answer 1

The rule of the loan is

`P=(L((r)/(n)))/(\lbrack1-(1+(r)/(n))^(-nt)\rbrack)`

P is the monthly payment

L is the loan amount

r is the rate in decimal

n is the number of periods per year

t is the time

Since you afford $1200 per month, then

P = 1200

Since the loan interest is 7%, then

r = 7/100 = 0.07

n = 12

Since the time is 30 years, then

t = 30

Substitute them in the rule above to find L

a)

`\begin{gathered} 1200=(L((0.07)/(12)))/(\lbrack1-(1+(0.07)/(12))^(-12(30))\rbrack) \\ 1200\lbrack1-((1207)/(1200))^(-360)\rbrack=L((0.07)/(12)) \\ (1200\lbrack1-((1207)/(1200))^(-360)\rbrack)/((0.07)/(12))=L \\ 180369.0815=L \end{gathered}`

The amount of the loan is $180 369.0815

b)

You can find the total money you will pay the loan company, multiply P by n by t.

`\begin{gathered} \text{Total}=1200*12*30 \\ \text{Total}=432000 \end{gathered}`

You will pay a total amount of $432 000

c)

The amount of interest is the difference between the total payment and the amount of the loan

`\begin{gathered} I=T-L \\ I=432000-180369.0815 \\ I=251630.9185 \end{gathered}`

The interest is $251 630.9185