Question

PLEASE HELP QUICK!

Answer 1

Brady has a 20-year fixed rate mortgage for $215,500 with monthly payments of $1,305.89. The annual interest rate is 4%. What is the total cost of the principal and interest for this loan rounded to the nearest dollar?

$172,400

$224,120

$313,414

$391,767

Answer 2

\(\bf \large balance = principal\left(1+\frac{r}{n}\right)^{nt}\)

r = APR in decimal format, 5% = 0.05
t = years
n = periods per year, annual compounding means once per year or 1 period per year

Answer 3

THANKS :)

Answer 4

what do i put as the principal? 215,500?

Answer 5

yes

Answer 6

okay and the n is 365?

Answer 7

well, they're using an annual interest rate, so I'd think is an APR
is not continously compound, just simple interest

so the periods per year is 1, the years 20

Answer 8

okay so it would end up being the ^20 ?

Answer 9

\(\bf balance = principal\left(1+\frac{r}{n}\right)^{nt} \implies balance = 215500(1+0.04)^{20}\)

Answer 10

isnt it .04 over 20?

Answer 11

it's an annual interest rate, or APR, annual percentage rate
is not being compounded, if it were compounded say monthly, then the period is 12, 12 periods/months per year

but if it's not compounded to less than that, then the period is 1, once per year

\(\bf balance = principal\left(1+\frac{r}{n}\right)^{nt} \implies balance = 215500\left(1+\frac{0.04}{1}\right)^{(1)20}\)

Answer 12

okay thanks let me calculate it hold on one sec :)

Answer 13

472,187.0373

Answer 14

that's the total principal after 20 years
the interest paid on it will be

new balance - old balance

the difference in the principals

Answer 15

okay thanks let me do that now :)

Answer 16

256,687.0373

Answer 17

right, don't forget, you're asked to provided rounded dollars :)

Answer 18

it doesnt give me any of my choices how would i do that exactly?

Answer 19

drop the float

Answer 20

472,187

and 256,687

Answer 21

thats not any of my answers. it gives me 215500

Answer 22

hmmm

Answer 23

what shall i do?

Answer 24

I'm thinking there's another equation for it

Answer 25

lemme look

Answer 26

okay

Answer 27

hmmm, lemme see
she's making monthly payments of 1305.89
she'll be doing that for the next 20 years

so she'll be paying 1305.89 for 240 months
so 1305.89 * 240 = 313,413.6

Answer 28

is that an option?

Answer 29

well, rounded should be $313,414