IB Mathematical Studies – Financial mathematics

1. IB Mathematical Studies, Simple Interest

How can we calculate the simple interest of a loan of $8000 at a rate of 5% per annum over 16 months?

Solution

IB Maths Studies SL, Simple Interest

The simple interest is given by the following formula

$I=P \cdot r \cdot n$

Where I is the amount of interest, P is the principal, r is the simple interest rate per annum and n is the time in years.

Regarding your question about the calculation of the simple interest, we have that

$I=$8000 \cdot 0.05 \cdot \frac{16}{12}=$533.33$

The guidelines for doing this exercise directly to GDC Casio FX-9860G is

TVM -> F1:Simple Interest -> n=(4/3)*365=486.67, I%=5, PV=-8000 and then press SI and get your result with a positive sign which is the simple interest.

2. Simple Interest Financial mathematics

IB Mathematical Studies SL, Simple Interest

How can we calculate the amount borrowed if the interest paid for this loan is $4,500 at a rate of 7% per annum over 48 months?

Solution

IB Maths Studies SL, Simple Interest

The simple interest is given by the following formula

$I=P \cdot r \cdot n$

Where I is the amount of interest, P is the principal, r is the simple interest rate per annum and n is the time in years.

Regarding your question about the calculation of the simple interest we have that $$4500=P \cdot 0.07 \cdot \frac{48}{12}=>P=\frac{4500}{0.28}=$16,071.43$

3. Compound Interest Financial mathematics

IB Mathematical Studies, Compound Interest

How can we calculate the interest paid on a deposit of $5,000 at 4% per annum compounded semi-annually for 24 months?

Solution

IB Mathematical Studies, Financial Mathematics, Compound Interest

Compounded semi-annually means interest is added to the principal semi-annually.

The general compounding formula is:

$F=P \cdot (1+ \frac{r}{100})^n$

and $I=P \cdot (1+ \frac{r}{100})^n -P$

Where F is the future value of the investment, P the principal (=$5,000), r is the interest rate per compound period (4/2=2%) and n is the number of compounding periods(24/6=4).

Regarding your question about the interest paid we will use the following formula

$I=5,000 \cdot (1+ \frac{2}{100})^4 -5000=412.16$

The guidelines for doing this exercise directly to GDC Casio FX-9860 is

TVM -> F2: Compound Interest -> n=4, I%=4, PV=5,000, P/Y=2, C/Y=2 and then press FV and get your result with a negative sign is FV and when this subtracted from the principal you get the interest.

4. IB Mathematical Studies, Financial Mathematics, Present value

How can we calculate the amount to be deposit into an account to collect $240,000 at the end of 3 years if the account is paying 8% per annum compounded every month?

Solution

IB Mathematical Studies, Financial Mathematics, Compound Interest, Present value

The general compounding formula is:

$F=P \cdot (1+ \frac{r}{100})^n$

Where F is the future value of the investment (=$40,000), P the principal, r is the interest rate per compound period ( $\frac{8}{12}=\frac{2}{3}$ ) and n is the number of compounding periods (=3*12=36 months).

Therefore, $$240,000=P \cdot (1+ \frac{2}{300})^36=>P=$188,941.11$

The guidelines for doing this exercise directly to GDC Casio FX-9860 is

TVM -> F2: Compound Interest -> n=36, I%=8, FV=240,000, P/Y=12, C/Y=12 and then press PV and get your result with a negative sign is PV.

IB Mathematics Studies, Financial Mathematics, Compound Interest

How can we calculate for how long the amount of $12,000 to be deposit into an account to collect $20,000 if the account is paying 5% per annum compounded quarterly?

Solution

IB Mathematical Studies, Compound Interest, a time period

The general compounding formula is:

$F=P \cdot (1+ \frac{r}{100})^n$

Where, F is the future value of the investment (=$20,000), P the principal (=$12,000), r is the interest rate per compound period ( $\frac{5}{4}$ ) and n is the number of compounding periods (unknown in our case).

Therefore, $$20,000=12,000 \cdot (1+ \frac{5}{400})^n=> n=41.12$ (using solver or graph)

The answer is approximately 41 quarters.

The guidelines for doing this exercise directly to GDC Casio FX-9860 is

TVM -> F2: Compound Interest -> I%=5, PV=12000, FV=-20000, P/Y=4, C/Y=4 and then press n and get the same result (=41.12).

5. IB Mathematical Studies, Financial Mathematics

How can we calculate for what annual rate of interest was paid for an amount of $24,000 to be deposit into an account that compounded quarterly and 2 years later the account totals $29,000?

Solution

IB Mathematical Studies, Financial Mathematics, the annual rate of interest

The general compounding formula is:

$F=P \cdot (1+ \frac{r}{100})^n$

Where F is the future value of the investment (=$29,000), P the principal (=$24,000), r is the interest rate per compound period (unknown in our case) and n is the number of compounding periods (2*4=8).

Therefore, $$29,000=$24,000 \cdot (1+ \frac{r}{100})^8=> r=2.3937 \ per \ quarter$ (using solver or graph) and then multiply this number by 4 and get the interest rate per annum $r_{a}=9.57%$

The guidelines for doing this exercise directly to GDC Casio FX-9860 is

TVM -> F2: Compound Interest -> PV=24000, FV=-29000, P/Y=4, C/Y=4, n=8 and then press I% and get the same result (9.57%).