# Mathematics

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A loan of \$7,000,000 is being amortised over 48 months at an interest rate of 12% compounded monthly. Find:
(a) the monthly payment;
(b) the principal outstanding at the beginning of the 36th month;
(c) the interest in the 36th payment;
(d) the principal in the 36th payment and
(e) the total interest paid.

• Mathematics -

You can tackle most monthly monthly payment questions with the following formula.

AR^n=P(R^n-1)/(R-1)
where
n=number of compounding periods
A=Amount borrowed
P=payment at each period
R=interest rate per period, in the form of 1.08 for 8%
For the given case,
A=7000000
R=1.01
n=48
(a)Solve for P to get \$184336.84 for the monthly payment
(b) The amount outstanding is the amount of the last payment less one month interest, \$184336.84/1.01=\$182511.72
(c) = difference between (a) and (b)
(d) = (b)
(e) = 48*(a)-7000000

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