Question

Your parents are buying a house for $187,500. They have a good credit rating, are
making a 20% down payment, and expect to pay $1,675/month. The interest rate for
the mortgage is 4.85%. What must their realized income be before each month and
how much interest is paid at the end of the second month? Be sure to include the
following in your response: the answer to the original question and the mathematical
steps for solving the problem demonstrating mathematical reasoning

Answer 1

@iGreen @saifoo.khan

Answer 2

First figure out how much they must borrow by getting rid of 20% of the cost of the home.
Use this amount and the formula I = Prt to find how much interest was accrued in the first
month. Add this amount to the borrowed total and then subtract the monthly payment. This
will be the principal at the beginning of the second month, so use it in the I = Prt formula to
find the interest accrued at the end of the second month. For the second part of the
question, their monthly payment should be no more than 28% of their realized income, so
take their payment and divide it by the 28%

Answer 3

@thomaster @bohotness

Answer 4

@UnkleRhaukus

Answer 5

@phi @ParthKohli

Answer 6

The good news is they gave us the instructions.
The bad news is you have to understand them, and do what they say.

Answer 7

ugh, thanks i been working on this question for days and it's hard to figure out.

Answer 8

The first step is we start with
$187,500
and make a "20% down payment"
any idea what that means ?

Answer 9

don't we have to divide that?

Answer 10

think like this:
you owe somebody $100
you pay them 20%
(which means you paid them 20% of 100, and that means 20/100 * 100 )
how much did you pay ?

Answer 11

How about you paid 1/5 of the bill i.e. you paid 1/5 of 100
how much did you pay ?

Answer 12

sorry computer froze, hold on.

Answer 13

so i did 20 / 100 * 100 and got 20 is that right?

Answer 14

yes. and notice 20/100 simplifies to 1/5 so 1/5 of 100 (or 100/5 = 20, same answer)

Answer 15

the idea is 20% is a fraction (20/100 , which may or not simplify)
and you are paying some fraction of the entire bill

examples: 10% of 50 is 10/100 * 50 or 1/10 * 50 = 5

how about 20% of 187500 ? any idea ?

Answer 16

no. i got nothing.

Answer 17

It's similar to the problem
1/2 of 4

Answer 18

How would you figure out
1/2 of 4 ?

Answer 19

it's 2

Answer 20

and the way you figure it out is multiply:
\[\frac{1}{2} \cdot 4 = 2 \]
can you do
3/4 of 4 ?

Answer 21

3

Answer 22

now use that same idea with
20/100 of 187500
bigger numbers, but the same idea. what do you get ?

Answer 23

37500

Answer 24

that means 20% of 187500 is 37500
that is how much was paid "up front" which means was paid immediately.
How much is left to pay ? any idea ?

Answer 25

i have no idea

Answer 26

if you owed 100 and paid 20, how much is left to pay ?

Answer 27

80

Answer 28

How did you figure that out ?

Answer 29

well if i owed 100 and only paid 20 i subtract 100 from 20 and get 80 so i owe 80

Answer 30

exactly.
now use that same idea, but with bigger numbers
you owed 187500 and paid 37500
how much is left to pay ?

Answer 31

150,000

Answer 32

that is the answer to the first question
First figure out how much they must borrow by getting rid of 20% of the cost of the home.
the answer is 150000

Answer 33

thank you.

Answer 34

Now the next step

Use this amount and the formula I = Prt to find how much interest was accrued in the first month.

when you borrow money they call the amount P (for principal)
Here , P = 150000 (we just figured this out)
r is the "rate"
t is the "time"

Answer 35

yeah p= 150000

Answer 36

what numbers should we use for r and t ?

Answer 37

i have no idea.

Answer 38

The interest rate for the mortgage is 4.85%
does that help for finding what r is ?

Answer 39

yes sir.

Answer 40

what is r ?

Answer 41

so 150000 / 4.85% ?

Answer 42

7275?

Answer 43

when you see % you first change it to a fraction
4.85% becomes 4.85/100 = 0.0485 (as a decimal)

next, this is rate is for a full year. we want the monthly rate
so we divide by 12 (12 months in a year)
that means
\[ r= \frac{0.0485}{12} \]
t (time) is 1 month
so use t=1

Answer 44

Here is what you know:
p= 150000
r= 0.0485/12
t=1
now figure out
I= p*r*t
(which means multiply p times r times t, using those numbers instead of the letters)

Answer 45

606.25

Answer 46

you found
I = 606.25
that is the interest that we add to the amount owed at the end of 1 month
in other words, the amount owed after one month is
150000+606.25

Answer 47

150606.25

Answer 48

so far we did this:
Add this amount to the borrowed total

the next step is to do this:
and then subtract the monthly payment.

Answer 49

read the question to find the monthly payment
what is the monthly payment ?

Answer 50

148931.25

Answer 51

yes, the payment is 1675 and we do
150606.25 - 1675= 148931.25

Answer 52

yeah that is what i did.

Answer 53

according to the question, they say
** This will be the principal at the beginning of the second month,**
so after one month, and making a payment, they now owe

p= 148931.25

can you figure out the interest using
I = p*r*t
where r and t are the same as the first time, but we have a new p ?

Answer 54

601.93

Answer 55

ok, that is the answer to this part:
how much interest is paid at the end of the second month?

the interest paid at the end of the second month is 601.93

Answer 56

The last part is this:
What must their realized income be?

The rule is that the payment is less than or equal to 28% of their income.
payment is 1675
we don't know their income, but we can give it a name: x
1675 is 28% of x

or
1675= 28/100 * x
to "find x"
we multiply both sides by 100/28
\[ 1675 \cdot \frac{100}{28} = x \]