Question

Rs 60000 invested at a certain rate for a certain even number of years compounded annually, grows to rs 63654. To how much amount would it grow if it is invested at the same rate for half the period?

Answer 1

Answer:

Rs 61800

Step-by-step explanation:

The amount A after compounding a principal amount P for n years using an interest rate i is;

$A=P*(1+\frac{i}{100})^n$

Now, we are given

P=60000

A=63654

assume that

n=t

i=i

And let the compounding factor for t years be denoted as X

Then;

$A=P*X^t\\63654=60000*X^t\\X^t=\frac{63654}{60000}\\ X^t=1.0609$

When the same amount is invested for half the period, n becomes 0.5t

Therefore the compounding factor becomes

$X^{\frac{t}{2}}=1.0609^{\frac{1}{2}}\\  X^{\frac{t}{2}}=1.03$

The new amount can be computed as;

$A=P*X^{\frac{t}{2}}\\A=60000*X^{\frac{t}{2}}\\A=60000*1.03\\A=61800$

ie

Rs 61800