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]

Question

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ To find the future value for 3 years, we use the formula: $FV = PV \left(1 + \frac{i}{f} ight)^{fn}$ ‖ ‖ step 2 ⋮ Given: $PV = 650000$, $i = 0.08$, $f = 2$ (semiannual), $n = 3$ years ‖ ‖ step 3 ⋮ Substitute the values: $FV = 650000 \left(1 + \frac{0.08}{2} ight)^{2 \cdot 3}$ ‖ ‖ step 4 ⋮ Calculate: $FV = 650000 \left(1 + 0.04 ight)^6 = 650000 \left(1.04 ight)^6 \approx 650000 imes 1.265319 = 822457.35$ ‖ ∻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: $FV = PV \left(1 + \frac{i}{f} ight)^{fn}$ ‖ ‖ step 2 ⋮ Given: $PV = 650000$, $i = 0.08$, $f = 2$ (semiannual), $n = 6$ years ‖ ‖ step 3 ⋮ Substitute the values: $FV = 650000 \left(1 + \frac{0.08}{2} ight)^{2 \cdot 6}$ ‖ ‖ step 4 ⋮ Calculate: $FV = 650000 \left(1 + 0.04 ight)^12 = 650000 \left(1.04 ight)^{12} \approx 650000 imes 1.601032 = 1040670.80$ ‖ ∻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: $FV_{6 ext{ years}} = 1040670.80$, $FV_{3 ext{ years}} = 822457.35$ ‖ ‖ 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◊What formula would you use to calculate the compound amount of an investment given the interest rate and compounding frequency?⍭ Generate me a similar question◊⚹

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