IB Maths AI SL AI 1.2 Sequences and financial mathematics questions

Exam-style questions in the shape of Paper 1 and Paper 2, with full markschemes. Read the markscheme, or type, photograph or draw your answer and get it marked.

Paper

Paper 1 Paper 2

Difficulty

Easy Medium Hard

Question 1

Paper 1Medium6 marks

Maya borrows $3,800 to repay a credit-card balance. Interest is charged at a nominal annual rate of 18.6%, compounded monthly. Maya pays$ 240 at the end of each month unless this would exceed the amount then owed, in which case she pays only the amount needed to clear the balance. There are no fees or further charges.

Give monetary amounts to the nearest cent.

(a)

Use the financial package on a graphic display calculator to determine the number of monthly payments Maya makes before the loan is cleared.

[2]

(b)

Using your answer to part (a),

(i)

find the amount of Maya’s final payment.

[2]

(ii)

hence calculate the total interest Maya pays over the loan.

[2]

Question 2

Paper 1Medium7 marks

The Northgate Credit Union offers simple interest at 2.7% per year on the original deposit. Leila deposits $2400 and makes no further deposits or withdrawals. Let $B_n$ be the balance, in dollars, at the end of $n$ years.

(a)

Calculate the common difference between consecutive year-end balances.

[1]

(b)

Show that $B_n=2400+64.80n$

[2]

(c)

Hence, determine the first whole year at the end of which the balance exceeds $3000.

[1]

(d)

A report summarizes the mean of the balances at the ends of years 1 to 10. Write the sum of these balances in sigma notation and hence determine the mean.

[3]

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