Maths Question 10 points

Let n be the number of months required to settle the loan.

At the end of the nth month, total amount required to be paid

= 10 000(1 + 18%/12)n

= 10 000(1.015)n

By the time, the amount repaid = 3000n

For the repayments are needed to settle the loan,

10 000(1.015)n - 3000n = 0

10(1.015)n - 3n = 0

This is impossible to be solved in analytical method, instead, we use trial and error.

When n = 3, L.H.S. = 1.457 > 0

When n = 4, L.H.S. = -1.386 < 0

Therefore, the minimum month required is 4 months.

And the repayment is: 10 000(1 + 18%/12)4 = $10 613.64 (cor. to 2 d.p.)