Home / IB Mathematics SL 1.4 Financial applications AA SL Paper 1- Exam Style Questions

IB Mathematics SL 1.4 Financial applications AA SL Paper 1- Exam Style Questions

IB Mathematics SL 1.4 Financial applications AA SL Paper 1- Exam Style Questions- New Syllabus

Question

Give answers to the nearest whole number.

Shahid invested 25,000 SGD in a fixed deposit account with a nominal annual interest rate of 3.6%, compounded monthly.

Part (a):
Calculate the value of Shahid’s investment after 5 years. [3]

After 5 years, Shahid withdrew \( x \) SGD and reinvested it in a super-savings account with a nominal annual interest rate of 5.7%, compounded half-yearly. The super-savings account increased to 20,000 SGD after 18 months.

Part (b):
Find the value of \( x \). [3]

▶️ Answer/Explanation
Detailed Solutions

Part (a) [3 marks]

Method 1: Use compound interest formula: \( FV = PV \cdot \left(1 + \frac{r}{n}\right)^{n \cdot t} \).

\( PV = 25,000 \), \( r = \frac{3.6}{100} = 0.036 \), \( n = 12 \), \( t = 5 \).

\[ FV = 25,000 \cdot \left(1 + \frac{0.036}{12}\right)^{12 \cdot 5} = 25,000 \cdot (1.003)^{60} \]

\[ FV \approx 29,922 \text{ SGD} \]

Method 2: Financial calculator settings:

Option 1: \( N = 5 \), \( I\% = 3.6 \), \( PV = -25,000 \), \( P/Y = 1 \), \( C/Y = 12 \).

Option 2: \( N = 60 \), \( I\% = 3.6 \), \( PV = -25,000 \), \( P/Y = 12 \), \( C/Y = 12 \).

Result: \( FV \approx 29,922 \text{ SGD} \).

Part (b) [3 marks]

Method 1: Use compound interest formula: \( FV = PV \cdot \left(1 + \frac{r}{n}\right)^{n \cdot t} \).

\( FV = 20,000 \), \( r = \frac{5.7}{100} = 0.057 \), \( n = 2 \), \( t = 1.5 \).

\[ 20,000 = x \cdot \left(1 + \frac{0.057}{2}\right)^{2 \cdot 1.5} = x \cdot (1.0285)^3 \]

\[ x = \frac{20,000}{(1.0285)^3} \approx 18,383 \text{ SGD} \]

Method 2: Financial calculator settings:

Option 1: \( N = 1.5 \), \( I\% = 5.7 \), \( FV = 20,000 \), \( P/Y = 1 \), \( C/Y = 2 \).

Option 2: \( N = 3 \), \( I\% = 5.7 \), \( FV = 20,000 \), \( P/Y = 2 \), \( C/Y = 2 \).

Result: \( x \approx 18,383 \text{ SGD} \).

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