# Interest Rates (Financing)

I am not sure how to tackle this problem. Could one explain how to do this the long way (like finding all the interests and subtracting) and how to do it with a formula. I just want to learn how to do this.

"Robyn borrows \$10000 from a bank. Interest at 18% per annum is calculated monthly on the amount of money still owing. Robyn repays \$600 each month. How much does Robyn owe the bank after the first 12 repayments?"

I am not sure if one should first find the interest and then subtract 600 or the other way around. And then where to go from this. If anyone can help me grab the idea behind this finance problems it will really be helpful.
###### Who is Participating?

x

Commented:
The answer in you book has not used compund interest just 1.5% per month which is just 18%/12 . This would give you this:

Month       Carried Fwd               Interest                     Reypayment
1      10000              150                 600
2      9550               143.25             600
3      9093.25           136.39875       600
4      8629.64875      129.4447313      600
5      8159.093481      122.3864022      600
6      7681.479883      115.2221983      600
7      7196.702082      107.9505312      600
8      6704.652613      100.5697892      600
9      6205.222402      93.07833603      600
10      5698.300738      85.47451107      600
11      5183.775249      77.75662874      600
12      4661.531878      69.92297817      600
4131.454856

After the 12th month's payment he owes \$4131.45
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Commented:
Mortgage Payments Components: Let where P = principal, r = interest rate per period, n = number of periods, k = number of payments, R = monthly payment, and D = debt balance after K payments, then

R = P × r / [1 - (1 + r)-n]

and

D = P × (1 + r)k - R × [(1 + r)k - 1)/r]

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Commented:
Hi cgomiz,

P = principal
Ins = installment

The basic idea is

At end of first month, borrower owes P + interest (for one month) on P
Of this amount he pays back Ins ... A part of Ins would make up for interest on P (say X) and remaining (Ins-X) would repay the principal
Hence, after first month, principal comes down to (P - (Ins - X))

For month2
borrower owes (P-(Ins-X)) + interest (for one month) on (P-(Ins-X))
And so on so forth ...

As you might have observed, as time progresses, the interest component in the repayment goes down.

Cheers!
sunnycoder
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Author Commented:
Raynard7 could you please proceed to show how my numbers fit into the equation? For example when trying out http://home.ubalt.edu/ntsbarsh/Business-stat/otherapplets/CompoundCal.htm#rjava4 it does not ask for my monthly payment. When checking the answer in the back of the book i have for this question it says 4131.45\$ I am lost
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Commented:
Robyn borrows \$10000 from a bank. Interest at 18% per annum is calculated monthly on the amount of money still owing. Robyn repays \$600 each month. How much does Robyn owe the bank after the first 12 repayments

You need to calculate the monthly interest x.
x^12 = 1.18
so
12 ln(x) = ln(1.18)
so
ln(x) = ln(1.18)/12
x = exp(ln(1.18)/12)
=1.013888
=1.3888% per month

Month       Carried Fwd               Interest                     Reypayment
1      10000                      138.8843035      600
2      9538.884303      132.4801303      600
3      9071.364434      125.9870131      600
4      8597.351447      119.4037168      600
5      8116.755164      112.7289887      600
6      7629.484152      105.9615592      600
7      7135.445712      99.10014077      600
8      6634.545852      92.14342796      600
9      6126.68928      85.09009734      600
10      5611.779378      77.93880702      600
11      5089.718185      70.6881965      600
12      4560.406381      63.33688639      600
4023.743268

After the 12th month's payment he owes \$4023.74
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Author Commented:
yes, you are right. JR 2003. I just fiddle with that 1.5% and i got it through this formula

10,000(1.015^12) -600(1+1.015+1.015^2+...+1.015^11)

K=1+1.015+1.015^2+...+1.015^11= (1-1.015^12)/(1-1.015)

plugged in the values in my calculator and got 4131.454856\$

thanks.

Question: what is the standard way to find the monthly interests (the way my book does it or the way JR2003 does it?)
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