Question

You have just grduated from college and landed youyr first job, you purchase a house cost 250,000 and find a bank interest rate 6% that compounds monthly for 30 years.
what is the monthly payment for this loan?
what is the unpaid balance at the end of 5 years?
what is the unpaid balance at the end of the 10th year?

I think I should use the formula A=p(1+I)n but I am not sure please help.

Answer 1

Yes yo do use that formula:\[C(t) = Co(1+r)^t\]
Where,
C(t) is the cost in the future
Co is the initial cost
r is the rate in decimals not % (6% = 0.06)
t is the time period, in this case in years.

Answer 2

I have A=250.000 (1+.06) 12
A=250.000 (1.06) 12
I don't know the next step

Answer 3

mathmind can yo help me when you're done

Answer 4

why did you put 12 as your t?

@btm2011, yes i'll try

Answer 5

I don't know should I put 30 cause thats the years

Answer 6

hmm not quite. Here we are making a formula of the Cost over the period of time t so,\[C(t)=250,000(1+.06)^t\]\[C(t) = 250,000(1.06)^t\]
this is the formula to find the cost at any time t (which is measure in years in this problem). If we want to know the unpaid balance at the end of 5 years, what do we do?

Answer 7

ummm take 250,000 (1.06) 5
i divide then multiply

Answer 8

what are you dividing ?

Answer 9

250,000 with (1.06)

Answer 10

that's a multiplication, isn't it?

Answer 11

ok so 250,000 (1.06) I got 265 then I divide that by 5

Answer 12

nope, do you know what a exponent is ? some number to the Nth power?

Answer 13

no

Answer 14

is that the 30 years

Answer 15

oh heck no. that is not the formula at all for paying off a loan. that is the formula for interest.

Answer 16

if i can figure out how to send an attachment i will send the correct formula.

Answer 17

last formula is the one you use for loan payments.

Answer 18

No, an exponent or power tells you how many times a number is multiplies by itself:\[2^2 = 2*2 = 4\]\[2^3 = 2*2*2 = 8\]\[2^4 = 2*2*2*2 = 16\] and so on..

so, what we have is:\[C(t)=250,000(1.06)^t\]in 5 years:\[C(5 years)=250,000(1.06)^{5years}\]\[C(5)= 250,000(1.06*1.06*1.06*1.06*1.06) = 334,556.39\]Hence, the unpaind balance would be:
334,556.39 - 25000 = 84556.4

Answer 19

that's not it ? which one is it then?

Answer 20

I got 8.833

Answer 21

this is just not right. You are answering the following question:
"if you invest $250,000 at 6% compounded monthly, how much will you have in 30 years"
this question says something different. "What are your monthly payments?"

Answer 22

@ Satellite73 yes and it then ask for the unpaid balance after 5 years and 10 years

Answer 23

\[PMT=\frac{250000\times \frac{.06}{12}}{(1-(1+\frac{.06}{12})^{-12\times 30}}\]

Answer 24

i got $1498.88 rounded. i can try again, but this sounds about right.

Answer 25

sio take 250000 multiply by .06 then divide by 12

Answer 26

as you can see the formula is a bit complicated so you have to be careful when entering it into a calculator. lots of room for mistake.

Answer 27

mathmind, can you please help me

Answer 28

do I divide .06 with 12 first then multiply the answer by 250000

Answer 29

that is your numerator. order does not matter. multiply by 250000 by .06 then divide by 12
or divide .06 by 12 then multiply by 250000 get the same thing

Answer 30

the denominator is much trickier. if you have a good calculator put it all in at once. be careful with parenthese

Answer 31

I don't have one with me

Answer 32

then you certainly cannot do this. you cannot compute these things by hand.

Answer 33

I have a regular one not one that you are aking if I have

Answer 34

what kind?

Answer 35

just a regular made in china hybrid power one

Answer 36

then you have to use lots of parentheses.

Answer 37

ok I am tryn but just can't get this