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.

- anonymous

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- anonymous

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.

- anonymous

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

- anonymous

mathmind can yo help me when you're done

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## More answers

- anonymous

why did you put 12 as your t?
@btm2011, yes i'll try

- anonymous

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

- anonymous

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?

- anonymous

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

- anonymous

what are you dividing ?

- anonymous

250,000 with (1.06)

- anonymous

that's a multiplication, isn't it?

- anonymous

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

- anonymous

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

- anonymous

no

- anonymous

is that the 30 years

- anonymous

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

- anonymous

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

- anonymous

last formula is the one you use for loan payments.

##### 1 Attachment

- anonymous

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

- anonymous

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

- anonymous

I got 8.833

- anonymous

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?"

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

sio take 250000 multiply by .06 then divide by 12

- anonymous

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.

- anonymous

mathmind, can you please help me

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

I don't have one with me

- anonymous

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

- anonymous

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

- anonymous

what kind?

- anonymous

just a regular made in china hybrid power one

- anonymous

then you have to use lots of parentheses.

- anonymous

ok I am tryn but just can't get this

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