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What is the monthly payment?

6 Answers
I rly need help with this math problem ! Fax machine cost $2670. It will be paid off in 18 months at 9% interest. What is the monthly payment?
M

I don't know about others, but your question is quite clear to me. You want to buy a Fax machine which costs $2670. You want to take loan for this amount at 9% interest rate and the repayment tenure is 18 months. You want to find out EMI. Isn't it?

I would like you to enquire the financer about the type of interest for this loan. There are two types of interests, simple and compund. Simple Interest is calculated on the principal only whereas compound interest is calculated on initial principal & also the accumulated interest of prior periods.

Say ,P= principal loan amount , r = annual rate of interest (as decimal), R = r/12 = monthly interest rate, n = tenure in months, t= tenure in years= m/12, M= equated monthly installment

The calculaton for amount of monthly payment is
M = {P * R * (1 + R)^n } / {(1 + R)^n - 1}

In your case, the principal is P = $2670, the monthly interest rate is R = 9%/12 = 0.0075, and the number of payments is n= 18. The monthly payment formula gives
M = { 2670 *0 .0075 * (1+0.0075)^18} / {(1+0.0075)^18 - 1} = $159.13

Now when we consider compund interest, interest may be compounded quarterly, monthly, weekly, daily, or even more frequently. Ask your finacer about the frequency of compounding.
Lets say,t he number of times per year that the interest is compounded = q (q =12 if compounded monthly, q =4 if compounded quarterly)

M = [P* r *{1 + (r/q)}^tq ] / [ q*{(1 + (r/q))^tq - 1}]

In your case if interest is compounded monthly then q=12, the principal is P = $2670, the yearly interest rate is r = 9% = 0.09, and the number of years is t = 18/12. The monthly payment formula gives
M = [2670 * 0.09 * { 1+ (.09/12)}^12*18/12] / [ 1*{(1+(.09/12))^12*18/12 - 1}] = $159.13
But if it compounded quarterly then q=4,
M = [2670 * 0.09 * { 1+ (.09/4)}^4*18/12] / [ 1*{(1+(.09/4))^4*18/12 - 1}] = $160.23
But if it compounded half yearly then q=2,
M = [2670 * 0.09 * { 1+ (.09/2)}^2*18/12] / [ 1*{(1+(.09/2))^2*18/12 - 1}] = $161.88

This gives an ideal that even if you are taking the loan in compound interest rate, make sure that the reducing balance EMI is as frequent as possible (daily reducing is the best). Good luck.

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F

I put my answer on the last question you posted - copied here for clarity:

I slightly disagree with Facers27 figures, but my answer is close. My working is as follows:

total owed = s[n] where n is how many months since the agreement started.

so s[0] = 2670
and s[1] = s[0] x i - k
where i is the monthly interest rate and k is the monthly repayment amount

then s[2] = (s[0] x i - k) x i - k = s[0] x i^2 -k (1+i)
and s[3] = (s[0] x i^2 - k(1+i) x i - k = s[0] x i^3 - k (1 + i + i^2)

and generally:
s[n] = s[0] x i^n - k (1 + i + i^2 + i^3 + ... +i^(n-1) )

suppose we let p = 1+i+i^2+i^3+...+i^(n-1)
then ip = i+i^2+i^3+...+i^n = p-1+i^n
but if ip=p-1+i^n
then p(i-1)=i^n-1
so p = (i^n -1)/(i-1)

we're looking at the situation after the 18th month, when it will be paid off, so s[18]=0
but we know that s[18] = s[0] x i^18 - kp

when n is 18, p is (i^18 -1)/(i-1)
and i is (1.09)^(1/12)
so putting numbers in gives us p = 19.14628
we know that s[18] = 0 and s[0] = 2670, so we get:
0 = 2670 x 1.137993 - k (19.14628)
so k = 2670 x 1.137993 / 19.14628
k = 158.6963.

So the amount paid will be 158.70 per month until the last month, when the total outstanding amount of 158.63 will be paid.

Total amount paid over the whole period is: 2856.53

Total interest paid is 186.53

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K

I used a personal loan calculator and your monthly payments would be $159 per month.

http://www.banksite.com/calcs/personalcalc.html

If you need to show your work, you will have to find a calculator that will show the amortization tables.

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F

The monthly repayment amount will be $159.13 per month.



Payment » $159.13
Number of Payments » 18
Total Paid » $2,864
Total Interest » $194

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M

I answered your question on the last post you made regarding this, not sure if you saw it. :-)

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S

U questions as no clarity

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