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Worked solution

Sum increasing interest-free instalments

Sonia buys a car with an interest-free loan of PP dollars. Monthly instalments start at $1200 and rise by $50 each month ($1250, $1300, …). The final instalment is $3250 and the loan is repaid in kk instalments. Find kk and PP.

[2009/SAJC/Promo/13(a)]

CJC · Discussion · Question 4

Answer

k=42k=42, P=93450P=93450 dollars.

Find the number of instalments

The instalments form an AP with a=1200a=1200, d=50d=50. Thus 1200+(k−1)50=32501200+(k-1)50=3250, giving k=42k=42.

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Sum the complete repayment

P=422(1200+3250)=93450P=\tfrac{42}2(1200+3250)=93450. The interest-free condition makes this sum equal to the original loan.

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Common mistakes

There are k−1 increases between the first and kth instalments.

Read the hint