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 2Easy6 marks

At the beginning of year 1, a savings account contains $6000. At the beginning of each following year,$ 500 is added to the account. The account pays simple interest at 4% per year on the amount deposited. Interest is withdrawn at the end of each year and is not added to the amount on which interest is calculated.

(a)

Calculate the interest earned in year 2.

[1]

(b)

State the first term and the common difference of the sequence of annual interest amounts.

[2]

(c)

Hence, write the total interest earned over the first 6 years using sigma notation, and calculate this total.

[3]

Question 2

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 3

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]

The best questions are still waiting

Unlock every question in this topic, then type, photograph or draw your answer and have it marked against the markscheme. Find out where you are dropping marks.

Unlock all questions Compare Student and Student Plus