IB Questionbank

Updates to Questionbank

User interface language: English | Español

Date	May Specimen paper	Marks available	3	Reference code	SPM.2.SL.TZ0.3
Level	Standard Level	Paper	Paper 2	Time zone	Time zone 0
Command term	Find	Question number	3	Adapted from	N/A

Question

On 1st January 2020, Laurie invests $P in an account that pays a nominal annual interest rate of 5.5 %, compounded quarterly.

The amount of money in Laurie’s account at the end of each year follows a geometric sequence with common ratio, r.

Find the value of r, giving your answer to four significant figures.

[3]

a.

Laurie makes no further deposits to or withdrawals from the account.

Find the year in which the amount of money in Laurie’s account will become double the amount she invested.

[3]

b.

Markscheme

${\left( {1 + \frac{{5.5}}{{4 \times 100}}} \right)^4}$ (M1)(A1)

1.056 A1

[3 marks]

a.

EITHER

$2P = P \times {\left( {1 + \frac{{5.5}}{{100 \times 4}}} \right)^{4n}}$ OR $2P = P \times {\left( {{\text{their}}\,\left( a \right)} \right)^m}$ (M1)(A1)

Note: Award (M1) for substitution into loan payment formula. Award (A1) for correct substitution.

OR

PV = ±1
FV = $\mp$ 1
I% = 5.5
P/Y = 4
C/Y = 4
n = 50.756… (M1)(A1)

OR

PV = ±1
FV = $\mp$ 2
I% = 100(their (a) − 1)
P/Y = 1
C/Y = 1 (M1)(A1)

THEN

⇒ 12.7 years

Laurie will have double the amount she invested during 2032 A1

[3 marks]

b.

Examiners report

[N/A]

a.

[N/A]

b.

Syllabus sections

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

Show 31 related questions

22M.2.SL.TZ1.1c:
Find the interest David will earn over the $10$ years.
18M.1.SL.TZ2.T_5a.ii:
Write down the amount of interest he earned after 5 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.
17M.1.SL.TZ2.T_14a:
Write down the amount of money Jashanti saves per month.
17N.1.SL.TZ0.T_9a:
Calculate the original price of the bicycle.
SPM.2.SL.TZ0.3a:
Find the value of r, giving your answer to four significant figures.
17N.2.AHL.TZ0.H_12b:
Show that the total value of Phil’s savings after 20 years is $\frac{{({{1.02}^{20}} - 1)P}}{{(1.02 - 1)}}$ .
17N.1.SL.TZ0.T_9b:
Calculate the difference between the original price of the bicycle and the total amount Juan will pay.
22M.2.SL.TZ1.1b:
Find the value of $r$ required so that the amount in David’s account after $10$ years will be equal to the amount in Sam’s account.
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.
EXN.2.SL.TZ0.7c.i:
Find the value of $N$ .
EXN.2.SL.TZ0.7b:
Given that $J_{n}$ follows a geometric sequence, state the value of the common ratio, $r$ .
EXN.2.SL.TZ0.7d:
Find Jane’s total earnings at the start of her $10$ th year of employment. Give your answer correct to the nearest dollar.
21M.2.SL.TZ1.7a.ii:
Determine the number of years required for Amelia’s investment to reach the target.
21M.2.SL.TZ1.7c.ii:
Find the amount Chris needs to deposit initially in order to reach the target after $5$ years. Give your answer to the nearest dollar.
21M.2.SL.TZ1.7c.i:
Show that Chris will never reach the target if his initial deposit is $$ 9000$ .
18M.1.SL.TZ2.T_5b:
Karl decides to donate this interest to a charity in France. The charity receives 170 euros (EUR). The exchange rate is 1 USD = t EUR.

Calculate the value of t.
EXN.2.SL.TZ0.7a:
Show that $H_{n} = 2400 n + 67 600$ .
17N.2.AHL.TZ0.H_12a:
Find the amount Phil would owe the bank after 20 years. Give your answer to the nearest dollar.
EXN.2.SL.TZ0.7c.ii:
For the value of $N$ found in part (c) (i), state Helen’s annual salary and Jane’s annual salary, correct to the nearest dollar.
22M.2.SL.TZ1.1a:
Find the amount that Sam will have in his account after $10$ years.
22M.2.SL.TZ2.3a:
Find Gemma’s annual salary for the year 2021, to the nearest dollar.
19M.2.SL.TZ2.T_6a:
Determine the amount that he will have in his account after 3 years. Give your answer correct to two decimal places.
19M.2.SL.TZ2.T_6c:
After $m$ complete months Tommaso will, for the first time, have enough money in his account to buy the bicycle.

Find the value of $m$ .
20N.1.SL.TZ0.T_8a:
Calculate the value of Imon’s investment after $5$ years.
21M.2.SL.TZ1.7a.i:
Find the value of Amelia’s investment after $5$ years to the nearest hundred dollars.
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 $x$ .
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

$\frac{{5000}}{{1.028}} + \frac{{5000}}{{{{1.028}^2}}} + \ldots + \frac{{5000}}{{{{1.028}^n}}}$ .
21M.2.SL.TZ1.7b:
Bill invests his $$ 9000$ in an account that offers an interest rate of $r %$ per annum compounded monthly, where $r$ is set to two decimal places.

Find the minimum value of $r$ needed for Bill to reach the target after $10$ years.
19M.2.SL.TZ2.T_6b:
Find the difference between the cost of the bicycle and the amount of money in Tommaso’s account after 3 years. Give your answer correct to two decimal places.
18M.1.SL.TZ2.T_5a.i:
Calculate the amount of money he has in the account after 5 years.

Hide related questions

Topic 1—Number and algebra