The balance is ₹0 at t = 0.

Question 105

MediumOriginal question

A savings account earns interest at 5% a year, compounded continuously, and money is paid in continuously at the rate of ₹12,000 a year. The balance $A$ (in rupees) after $t$ years satisfies $\frac{dA}{dt} = \frac{A}{20} + 12{,}000$ .

The balance is ₹0 at $t = 0$ . What is the balance after 20 years?

₹

600(e - 1)

Correct answerYour answer₹

2{,}40{,}000

Correct answerYour answer₹

2{,}40{,}000(e - 1)

Correct answerYour answer₹

2{,}40{,}000e

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

$A(0) = C - 2{,}40{,}000 = 0$ , so $C = 2{,}40{,}000$ and $A = 2{,}40{,}000\left(e^{t/20} - 1\right)$ .
At $t = 20$ : $A = 2{,}40{,}000(e - 1)$ .

Worth noting

₹2,40,000 is only the money paid in, $12{,}000 \times 20$ , with no interest.

Concept: A linear equation in a growth or mixing setting
Typical timeTypical: 120 s
Your timeYours: —

The rule this testsSolving linear equations

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Ten questions from Homogeneous & Linear Differential Equations, at your own pace.

Practise this chapter →

Ten questions from Homogeneous & Linear Differential Equations, at your own pace.

The balance is ₹0 at t = 0.

Question 105

Explanation