| Date | November 2019 | Marks available | 2 | Reference code | 19N.2.SL.TZ0.4 |
| Level | SL | Paper | 2 | Time zone | no time zone |
| Command term | Calculate | Question number | 4 | Adapted from | N/A |
Question
Investment planning is something that many people need to be aware of. Planning for your future requires research because bad choices can be very costly.
Interest paid on money invested is usually in the form of compound interest. The formula to calculate compound interest is:
T is the total value of the investment,
P is the principal sum invested,
r is the interest rate per time period converted to a decimal (for example, 5 % is 0.05),
n is the number of time periods.
An additional $1000 is added to a principal amount of $30 000 at the end of each month.
The monthly interest rate is 0.5 % and this rate is compounded at the end of each month.
Each month, tax is calculated on the monthly profit at a rate of 25 % when the investment total (T) is $40 000, or below. However, when the investment total (T) is above $40 000, the tax rate is 40 %.
The tax is calculated at the end of each month after interest has been added. A running total of the tax is kept and only deducted from the investment total (T) at the end of the year.
Calculate the total value of the investment after two years if the principal sum of $30 000 is invested. The yearly interest rate is 10 % and this rate is compounded at the end of each year.
Outline, using a diagram or otherwise, a method of calculating the total value of the investment after 12 months.
Construct an algorithm to calculate the fund value at the end of each month. This algorithm should also calculate the total value of the investment after the tax has been deducted after 12 months.
Many investment companies offer alternative investment schemes and use modelling to set the rates of interest.
Explain why the investment company would use modelling when setting the rates of interest.
Markscheme
Award [2 max].
36300;
if interest only award [1 mark max], $6300;
Award [5 max].
Award [1] Initial investment 30000 for month 0;
Award [1] Investment 1000 each month;
Award [1] Interest rate of 0.005 * Principal
Award [1] Calculate compound interest for 12 months;
Award [1] Add interest to the investment;
Award [6 max].
An array does not need to be used to obtain full marks.
Award [1] Create array or variables / initialise array or variables / P[0] = 30 000;
Award [1] Create interest rate and assign it to 1.005;
Award [1] Calculate interest;
Award [1] Add interest and 1000 to each month;
Award [1] If statement to determine the correct tax rate;
Award [1] Output investment - tax;
Alternative solution without an array
Award [4 max].
A what if scenario can be employed;
A mathematical model will allow you to adjust variables to see what impact that will have on the investment;
You can see exactly what is happening to the money each month;
If the client decides to pay in less or more money for a given month you can see what affect this will have on the profits;
If the interest rate changes, you will be able to see what changes this has on profit;
If the tax rate changes you can see how this affects the investment profits.
