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Question 3
[Total: 20 marks]
a) Ron sold one of his properties for RM650,000 and he plans to use the profit margin of the sale for investment. He believes he can earn an interest of $8 \%$ compounded semiannually. Find the compound amount if he invests for:
i) 3 years
[4]
ii) 6 years
[4]
iii) Find the additional amount earned due to the longer period in a(ii).
[2]
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Answer from Sia

Posted 2 months ago

Solution by Steps

step 1

To find the future value for 3 years, we use the formula: $FV = PV \left(1 + \frac{i}{f}\right)^{fn}$

step 2

Given: $PV = 650000$, $i = 0.08$, $f = 2$ (semiannual), $n = 3$ years

step 3

Substitute the values: $FV = 650000 \left(1 + \frac{0.08}{2}\right)^{2 \cdot 3}$

step 4

Calculate: $FV = 650000 \left(1 + 0.04\right)^6 = 650000 \left(1.04\right)^6 \approx 650000 \times 1.265319 = 822457.35$

Answer

$822457.35$

Key Concept

Future Value Calculation

Explanation

The future value of an investment compounded semiannually for 3 years at an 8% interest rate is calculated using the compound interest formula.

Solution by Steps

step 1

To find the future value for 6 years, we use the same formula: $FV = PV \left(1 + \frac{i}{f}\right)^{fn}$

step 2

Given: $PV = 650000$, $i = 0.08$, $f = 2$ (semiannual), $n = 6$ years

step 3

Substitute the values: $FV = 650000 \left(1 + \frac{0.08}{2}\right)^{2 \cdot 6}$

step 4

Calculate: $FV = 650000 \left(1 + 0.04\right)^12 = 650000 \left(1.04\right)^{12} \approx 650000 \times 1.601032 = 1040670.80$

Answer

$1040670.80$

Key Concept

Future Value Calculation

Explanation

The future value of an investment compounded semiannually for 6 years at an 8% interest rate is calculated using the compound interest formula.

Solution by Steps

step 1

To find the additional amount earned due to the longer period, subtract the future value for 3 years from the future value for 6 years

step 2

Given: $FV_{6 \text{ years}} = 1040670.80$, $FV_{3 \text{ years}} = 822457.35$

step 3

Calculate: $Additional \, Amount = 1040670.80 - 822457.35 = 218213.45$

Answer

$218213.45$

Key Concept

Additional Amount Calculation

Explanation

The additional amount earned due to the longer investment period is found by subtracting the future value for 3 years from the future value for 6 years

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