QUESTION 5
Easy
If you have ₹800 and you save ₹250 every month, find the amount you have after (i) 6 months (ii) 2 years. Express this as a linear pattern.
SOLUTION
1
Identify initial amount and monthly addition
Initial amount = ₹\(800\)
Monthly savings = ₹\(250\)
Monthly savings = ₹\(250\)
2
Derive the linear expression for \(n^{th}\) month
At the end of \(n\) months, you will have saved money \(n\) times.
\( Amount = 800 + 250n\)
\( Amount = 800 + 250n\)
3
Find the amount after (i) 6 months and (ii) 2 years
(i) After \(6\) months,
\(\begin{aligned} \text{Amount} &= 800 + 250(6) \\ &= 800 + 1500 \\ &= 2300\end{aligned}\)
(i) After \(2\) years(\(24\) months),
\(\begin{aligned} \text{Amount} &= 800 + 250(24) \\ &= 800 + 6000 \\ &= 6800\end{aligned}\)
\(\begin{aligned} \text{Amount} &= 800 + 250(6) \\ &= 800 + 1500 \\ &= 2300\end{aligned}\)
(i) After \(2\) years(\(24\) months),
\(\begin{aligned} \text{Amount} &= 800 + 250(24) \\ &= 800 + 6000 \\ &= 6800\end{aligned}\)
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Final Answer :
Amount after (i)6 months: ₹2300, (ii) 2 years: ₹6800
Linear expression: \(800 + 250n\)
Concept Note
Find the linear expression and substitute \(n\) to find amount.