Yahoo Answers: Answers and Comments for Home work math help!? [Mathematics]
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From michelle
enUS
Thu, 18 Jul 2019 02:36:59 +0000
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Yahoo Answers: Answers and Comments for Home work math help!? [Mathematics]
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From Captain Matticus, LandPiratesInc: We can work out a 3 payment structure for a lo...
https://answers.yahoo.com/question/index?qid=20190718023659AArRm6w
https://answers.yahoo.com/question/index?qid=20190718023659AArRm6w
Thu, 18 Jul 2019 03:01:28 +0000
We can work out a 3 payment structure for a loan and then generalize that to an npayment structure
((L * (1 + i/12)  P) * (1 + i/12)  P) * (1 + i/12)  P = 0
Let 1 + i/12 = k
((Lk  P) * k  P) * k  P = 0
Solve for L
((Lk  P) * k  P) * k = P
(Lk  P) * k  P = P/k
(Lk  P) * k = P + P/k
Lk  P = P/k + P/k^2
Lk = P + P/k + P/k^2
L = P/k + P/k^2 + P/k^3
If this extended on through to an nnumber of payments, hopefully you could see how this would generalize to:
L = P/k + P/k^2 + P/k^3 + .... + P/k^n
But adding up all of those terms is annoying, so let's simplify it. Let 1/k = a
L = Pa + Pa^2 + Pa^3 + ... + Pa^n
L = P * (a + a^2 + a^3 + ... + a^n)
S = a + a^2 + a^3 + ... + a^n
Sa = a * (a + a^2 + a^3 + .... + a^n)
Sa = a^2 + a^3 + a^4 + ... + a^(n + 1)
Sa  S = a^2 + a^3 + ... + a^(n + 1)  (a + a^2 + ... + a^n)
S * (a  1) = a^2  a^2 + a^3  a^3 + ... + a^n  a^n + a^(n + 1)  a
S * (a  1) = 0 + 0 + 0 + ... + 0 + a^(n + 1)  a
S * (a  1) = a^(n + 1)  a
S * (a  1) = a * (a^(n)  1)
S = a * (a^(n)  1) / (a  1)
S = a * (1  a^(n)) / (1  a)
S = (1/k) * (1  (1/k)^n) / (1  (1/k))
S = (1/k) * (1  (1/k)^n) / ((k  1)/k)
S = (1  (1/k)^n) / (k  1)
S = (1  k^(n)) / (k  1)
L = P * S
L = P * (1  k^(n)) / (k  1)
L = P * (1  (1 + i/12)^(n)) / (1 + i/12  1)
L = P * (1  ((12 + i) / 12)^(n)) / (i/12)
L = 12 * P * (1  (12/(12 + i))^n) / i
L = loan amount
P = payment
i = annual interest rate
n = number of payments
L = 20000
P = ?
i = 6% = 0.06
n = 15 year * 12 months/year = 180 months
L = 12 * P * (1  (12/(12 + i))^n) / i
20000 = 12 * P * (1  (12/(12 + 0.06))^180) / 0.06
20000 * 0.06 / (12 * (1  (12/12.06)^180)) = P
P = 20000 * 0.01 / (2 * (1  (2/2.01)^180))
P = 200 / (2 * (1  (200/201)^180))
P = 100 / (1  (201/200)^(180))
P = 100 / (1  1.005^(180))
P = 168.77136560969026208686627213866...
Your monthly payment will be $168.77. Expect for it to be rounded up to 168.78 or even 169, just to make it a nice roundish number (that's real world expectation, where your final payment will be less than previous payments, but all of the other payments will be nicer to look at)
You're going to make 180 of those payments
180 * 100 / (1  1.005^(180)) = 30378.845809744247175635928984958
$30378.85
You'll pay 10378.85 in interest
10378.85 / 30378.85 = 0.34164714073551645564690222761633
34.165%, roughly in interest. The rest will be in principal. 1  0.34164714073551645564690222761633....

From TomV: p/P = i/(1  1/(1+i)^n)
p = periodic loan amor...
https://answers.yahoo.com/question/index?qid=20190718023659AArRm6w
https://answers.yahoo.com/question/index?qid=20190718023659AArRm6w
Thu, 18 Jul 2019 03:46:05 +0000
p/P = i/(1  1/(1+i)^n)
p = periodic loan amortization payment
P = initial amount of loan
i = periodic interest rate = annual rate divided by number of payments per year
n = total number of periodic payments during the term of the loan
P = 20000
i = 0.06/12 = 0.005
n = 15*12 = 180
a. Calculate the monthly payment.
.p/P = 0.005/(1  1/(1.005)^180) = 0.0084386
Ans: p = 20000*0.0084386 = $168.77
b. Determine the total amount paid over the term of the loan.
180 payments at $168.77 = 30378.60
Ans: $30378.60
c. Of the total amount paid, what percentage is paid toward the principal and what percentage is paid for interest
$20000 paid toward the principal amount of the loan and 30378.60  20000 = 10378.60 paid toward interest.
Ans: 10378.60/30378.60 = 0.342 = 34.2% of total payment is interest.

From az_lender: (a) Monthly payment is $168.77, according to ...
https://answers.yahoo.com/question/index?qid=20190718023659AArRm6w
https://answers.yahoo.com/question/index?qid=20190718023659AArRm6w
Thu, 18 Jul 2019 02:43:51 +0000
(a) Monthly payment is $168.77, according to the Bret Whissel Amortization Calculator.
(b) The amount paid over the term of the loan is 180 x $168.77 = $30,378.60.
(c) Of the total amount paid, the percentage towards principal is 20000.00/30378.60 = 65.8%.
Therefore, the percentage towards interest is 100%  65.8% = 34.2%.

From Krishnamurthy: Consider a student loan of $20,000 at a fixed...
https://answers.yahoo.com/question/index?qid=20190718023659AArRm6w
https://answers.yahoo.com/question/index?qid=20190718023659AArRm6w
Thu, 18 Jul 2019 06:26:18 +0000
Consider a student loan of $20,000 at a fixed APR of 6% for 15 years.
a. Calculate the monthly payment.
b. Determine the total amount paid over the term of the loan.
c. Of the total amount paid, what percentage is paid toward the principal
and what percentage is paid for interest.
the monthly payment is $177.02
the total payment over the term of the loan is $63727.2
Now if you want what percent of each payment goes to principal you need to get what is called an amortization schedule. You can find these in many places such as Yahoo Finance. Of course in this case the percentage of payment going to principal will change with every payment. The percentage going to principle starts very small but at the end becomes almost 100%.