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# A man has a loan which he promised to pay in 18 equal monthly installments of P600. What are monthly installments for 8 months 10 months 12 months and 15 months?

The question can be answered only for the loan with zero interest.

The loan is then 10,800 (18 x 600) that could also be paid by

1350 a month for 8 months

1080 a month for 10 months

900 a month for 12 months

720 a month for 15 months

In the case the loan is not interest free the problem cannot be solved, since there are two unknown variables: a principal amount (an amount borrowed) and an annual interest rate and only one equation.

For instance if you borrow 10,000 with 10% annual interest rate, the loan will be paid off in 18 monthly installments of 600, which corresponds to the question. For the same principal (10,000) and annual interest rate (10%) the loan would have been paid off in:

8 month installments of 1297;

10 month installments of 1046;

12 month installments of 879;

15 month installments of 712.

But you can still have the loan with other pairs of principal and interest rate with 18 monthly installments of 600.

There is a suitable Excel formula PMT too.

Monthly installments can be calculated by formula:

Monthly installment = Principal x {rate + (rate / [(1+rate)months - 1]}

where rate = (annual rate / 12), i.e. 10% => 0,1/12 Study guides

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