With the balance ₹0 at t = 0, after how long…

With the balance ₹0 at t = 0, after how long does it reach ₹2,40,000?

Question 116

HardOriginal 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 $\frac{dA}{dt} = \frac{A}{20} + 12{,}000$ .

With the balance ₹0 at $t = 0$ , after how long does it reach ₹2,40,000?

\frac{\log 2}{20}

yearsCorrect answerYour answer

20\log 2

yearsCorrect answerYour answer20 yearsCorrect answerYour answer

20\log 3

yearsCorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

$2{,}40{,}000\left(e^{t/20} - 1\right) = 2{,}40{,}000$ gives $e^{t/20} = 2$ .
$\frac{t}{20} = \log 2$ , so $t = 20\log 2$ , about 13.9 years.

Worth noting

20 years counts the deposits alone; with interest the balance gets there sooner.

Concept: A linear equation in a growth or mixing setting
Typical timeTypical: 150 s
Your timeYours: —

The rule this testsSolving linear equations

Practise this chapter →

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.

With the balance ₹0 at t = 0, after how long does it reach ₹2,40,000?

Question 116

Explanation