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Date	May Example question	Marks available	3	Reference code	EXM.2.SL.TZ0.2
Level	Standard Level	Paper	Paper 2	Time zone	Time zone 0
Command term	Calculate	Question number	2	Adapted from	N/A

Question

Sophie is planning to buy a house. She needs to take out a mortgage for $120000. She is considering two possible options.

Option 1: Repay the mortgage over 20 years, at an annual interest rate of 5%, compounded annually.

Option 2: Pay $1000 every month, at an annual interest rate of 6%, compounded annually, until the loan is fully repaid.

Give a reason why Sophie might choose

Sophie decides to choose option 1. At the end of 10 years, the interest rate is changed to 7%, compounded annually.

Calculate the monthly repayment using option 1.

[2]

a.i.

Calculate the total amount Sophie would pay, using option 1.

[2]

a.ii.

Calculate the number of months it will take to repay the mortgage using option 2.

[3]

b.i.

Calculate the total amount Sophie would pay, using option 2.

[2]

b.ii.

option 1.

[1]

c.i.

option 2.

[1]

c.ii.

Use your answer to part (a)(i) to calculate the amount remaining on her mortgage after the first 10 years.

[2]

d.i.

Hence calculate her monthly repayment for the final 10 years.

[2]

d.ii.

Markscheme

evidence of using Finance solver on GDC M1

Monthly payment = $785 ($784.60) A1

[2 marks]

a.i.

$240 \times 785 = {\text{\$}}188000$ M1A1

[2 marks]

a.ii.

$N = 180.7$ M1A1

It will take 181 months A1

[3 marks]

b.i.

$181 \times 1000 = {\text{\$ }}181000$ M1A1

[2 marks]

b.ii.

The monthly repayment is lower, she might not be able to afford $1000 per month. R1

[1 mark]

c.i.

the total amount to repay is lower. R1

[1 mark]

c.ii.

$74400 (accept $74300) M1A1

[2 marks]

d.i.

Use of finance solver with N =120, PV = $74400, I = 7% A1

$855 (accept $854 − $856) A1

[2 marks]

d.ii.

Examiners report

[N/A]

a.i.

[N/A]

a.ii.

[N/A]

b.i.

[N/A]

b.ii.

[N/A]

c.i.

[N/A]

c.ii.

[N/A]

d.i.

[N/A]

d.ii.

Syllabus sections

Topic 1—Number and algebra » SL 1.7—Loan repayments and amortization

Show 34 related questions

EXM.2.SL.TZ0.1b.i:
the amount Paul pays each month.
EXM.2.SL.TZ0.2a.i:
Calculate the monthly repayment using option 1.
EXM.2.SL.TZ0.2c.ii:
option 2.
SPM.2.SL.TZ0.1a.i:
Find the repayment made each quarter.
EXM.2.SL.TZ0.2a.ii:
Calculate the total amount Sophie would pay, using option 1.
SPM.2.AHL.TZ0.3a.ii:
Find the total amount paid for the car.
22M.1.SL.TZ2.13b:
For option 2, find the minimum value of $x$ that Juliana would need to invest each year. Give your answer to the nearest dollar.
22M.1.SL.TZ2.13a:
For option 1, determine the minimum amount Juliana would need to invest. Give your answer to the nearest dollar.
21N.1.SL.TZ0.10b.i:
Find the amount Raul and Rosy will still owe the bank at the end of the first $10$ years.
EXM.2.SL.TZ0.1c.i:
option 1.
EXM.2.SL.TZ0.2d.i:
Use your answer to part (a)(i) to calculate the amount remaining on her mortgage after the first 10 years.
EXM.2.SL.TZ0.1b.ii:
the total amount that Paul has to pay.
EXM.2.SL.TZ0.1a.ii:
the total amount that Paul has to pay.
SPM.2.SL.TZ0.1a.iii:
Find the interest paid on the loan.
SPM.2.SL.TZ0.1b.i:
Find the amount to be borrowed for this option.
SPM.2.SL.TZ0.1a.ii:
Find the total amount paid for the car.
SPM.2.AHL.TZ0.3a.iii:
Find the interest paid on the loan.
SPM.2.AHL.TZ0.3a.i:
Find the repayment made each quarter.
SPM.2.SL.TZ0.1b.ii:
Find the annual interest rate, $r$ .
EXM.2.SL.TZ0.2c.i:
option 1.
EXM.2.SL.TZ0.2b.ii:
Calculate the total amount Sophie would pay, using option 2.
EXM.2.SL.TZ0.2d.ii:
Hence calculate her monthly repayment for the final 10 years.
SPM.2.AHL.TZ0.3b.i:
Find the amount to be borrowed for this option.
EXM.1.SL.TZ0.6a:
Calculate the amount Yejin needs to have saved into her annuity fund, in order to meet her retirement goal.
SPM.2.AHL.TZ0.3b.ii:
Find the annual interest rate, $r$ .
SPM.2.SL.TZ0.1c:
State which option Bryan should choose. Justify your answer.
SPM.2.AHL.TZ0.3c:
State which option Bryan should choose. Justify your answer.
EXM.2.SL.TZ0.1c.ii:
option 2.
EXM.1.SL.TZ0.6b:
Yejin has just turned 28 years old. She currently has no retirement savings. She wants to save part of her salary each month into her annuity fund.

Calculate the amount Yejin needs to save each month, to meet her retirement goal.
EXM.2.SL.TZ0.1a.i:
the number of months it will take for Paul to repay the loan.
SPM.2.AHL.TZ0.3d:
Bryan chooses option B. The car dealership invests the money Bryan pays as soon as they receive it.

If they invest it in an account paying 0.4 % interest per month and inflation is 0.1 % per month, calculate the real amount of money the car dealership has received by the end of the 6 year period.
SPM.2.SL.TZ0.1d:
Bryan’s car depreciates at an annual rate of 25 % per year.

Find the value of Bryan’s car six years after it is purchased.
21N.1.SL.TZ0.10a:
Find the amount they will pay the bank each month.
21N.1.SL.TZ0.10b.ii:
Using your answers to parts (a) and (b)(i), calculate how much interest they will have paid in total during the first $10$ years.

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Topic 1—Number and algebra

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Markscheme

Examiners report

Syllabus sections

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