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Date	May Example question	Marks available	3	Reference code	EXM.1.SL.TZ0.1
Level	Standard Level	Paper	Paper 1	Time zone	Time zone 0
Command term	Calculate	Question number	1	Adapted from	N/A

Question

Give your answers to this question correct to two decimal places.

Gen invests $2400 in a savings account that pays interest at a rate of 4% per year, compounded annually. She leaves the money in her account for 10 years, and she does not invest or withdraw any money during this time.

Calculate the value of her savings after 10 years.

[2]

a.

The rate of inflation during this 10 year period is 1.5% per year.

Calculate the real value of her savings after 10 years.

[3]

b.

Markscheme

$2400{\left( {1.04} \right)^{10}} = {\text{\$}}3552.59$ M1A1

[2 marks]

a.

real interest rate = $4 - 1.5 = 2.5{\text{% }}$ A1

$2400{\left( {1.025} \right)^{10}} = {\text{\$}}3072.20$ M1A1

[3 marks]

b.

Examiners report

[N/A]

a.

[N/A]

b.

Syllabus sections

Topic 1—Number and algebra » SL 1.4—Financial apps – compound interest, annual depreciation

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22M.2.SL.TZ2.2d.i:
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SPM.2.SL.TZ0.1a.i:
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18M.2.SL.TZ1.T_3b:
Calculate 14 000 USD in INR.
SPM.2.AHL.TZ0.3a.ii:
Find the total amount paid for the car.
22M.2.SL.TZ2.2d.ii:
Describe what the value in part (d)(i) represents in this context.
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.
17N.2.AHL.TZ0.H_12c:
Given that Phil’s aim is to own the house after 20 years, find the value for $P$ to the nearest dollar.
18M.1.SL.TZ2.T_4b:
Josh states: “Every integer is a natural number”.

Write down whether Josh’s statement is correct. Justify your answer.
19N.1.SL.TZ0.T_8a:
Calculate the value of Siân’s investment after four years. Give your answer correct to two decimal places.
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.
EXM.1.SL.TZ0.1a:
Calculate the value of her savings after 10 years.
SPM.2.SL.TZ0.1b.ii:
Find the annual interest rate, $r$ .
21M.2.SL.TZ1.3b:
Find the minimum value of $m$ , where $m \in ℕ$ .
18M.2.SL.TZ1.T_3d:
Harinder chose option B. At the end of five years, Harinder converted this investment back to USD. The exchange rate, at that time, was 1 USD = 67.16 INR.

Calculate how much more money, in USD, Harinder earned by choosing option B instead of option A.
17N.2.AHL.TZ0.H_12d.ii:
Hence or otherwise, find the minimum value of $Q$ that would permit David to withdraw annual amounts of $5000 indefinitely. Give your answer to the nearest dollar.
20N.1.SL.TZ0.T_8a:
Calculate the value of Imon’s investment after $5$ years.
SPM.2.AHL.TZ0.3b.i:
Find the amount to be borrowed for this option.
SPM.2.AHL.TZ0.3b.ii:
Find the annual interest rate, $r$ .
19N.1.SL.TZ0.T_8b:
After the four-year period, Siân withdraws $40\,000$ AUD from her savings account and uses this money to buy a car. It is known that the car will depreciate at a rate of $18$ % per year.

The value of the car will be $2500$ AUD after $t$ years.

Find the value of $t$ .
EXN.1.SL.TZ0.9b:
Find an approximation for the real interest rate for the money invested in the account.
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.
17N.2.AHL.TZ0.H_12a:
Find the amount Phil would owe the bank after 20 years. Give your answer to the nearest dollar.
21M.2.SL.TZ1.3d.ii:
the annual interest rate of the loan.
17N.2.AHL.TZ0.H_12b:
Show that the total value of Phil’s savings after 20 years is $\frac{{({{1.02}^{20}} - 1)P}}{{(1.02 - 1)}}$ .
18M.2.SL.TZ1.T_3c:
Calculate the amount of this investment, in INR, in this account after five years.
21M.1.SL.TZ2.10b:
Tommaso wants to invest his money in an account such that his investment will increase to $1.5$ times the initial amount in $5$ years. Assume the account pays a nominal annual interest of $r %$ compounded quarterly.

Determine the value of $r$ .
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.
21M.2.SL.TZ1.3c:
Write down the amount of the loan.
21M.2.SL.TZ1.3e:
Find the amount of Daisy’s final payment.
21M.2.SL.TZ1.3d.i:
the amount of interest paid by Daisy.
21M.2.SL.TZ1.3f:
Find how much money Daisy saved by making one final payment after $5$ years.
21M.2.SL.TZ1.3a:
Calculate the value of Daisy’s investment after $2$ years.
21M.1.SL.TZ2.10a:
Calculate the amount Pietro will have in his account after $5$ years. Give your answer correct to $2$ decimal places.
21M.1.AHL.TZ2.5a:
Estimate the value of Roger’s laptop after $5$ years.
21M.1.AHL.TZ2.5c:
Comment on the validity of your answer to part (b).
18M.2.SL.TZ1.T_3a:
Calculate the value of r.
17N.2.AHL.TZ0.H_12d.i:
David wishes to withdraw $5000 at the end of each year for a period of $n$ years. Show that an expression for the minimum value of $Q$ is

$\frac{{5000}}{{1.028}} + \frac{{5000}}{{{{1.028}^2}}} + \ldots + \frac{{5000}}{{{{1.028}^n}}}$ .
EXN.1.SL.TZ0.9a:
Find the value of her investment after a period of $5$ years.
EXN.1.SL.TZ0.9c:
Hence find the real value of Sophia’s investment at the end of $5$ years.
20N.1.SL.TZ0.T_8b:
At the end of the $5$ years, Imon withdrew $x SGD$ from the fixed deposit account and reinvested this into a super-savings account with a nominal annual interest rate of $5.7 %$ , compounded half-yearly.

The value of the super-savings account increased to $20 000 SGD$ after $18$ months.

Find the value of $x$ .
21M.1.AHL.TZ2.5b:
Find the value of $k$ .
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