Question

In how many years will a sum of Rs.3000 at 20% per annum compounded semi-annually become Rs.3993?

Answer 1

principal = Rs 3000
rate=10% compounded half yearly
time= T half years
amount = Rs 3993

P (1+R/100)^T=A
=>3000 (1+10/100)^T=3993
=>3000 (11/10)^T=3993
=>(11/10)^T=3993/1000
=>(11/10)^T=(11/10)^3
=>T=3

Time taken is 3 half years or 1 1/2 years.

Answer 2

Answer:

14.368 years

Step-by-step explanation:

Since, the amount, compounded semiannually for t years is,

$A=P(1+\frac{r/2}{100})^{2t}$

Where, r is the annual rate,

P is the principal amount,

Given,

P = 3000 rupees,

r = 20 %

A = 3993,

$3993 = 3000(1+\frac{20}{200})^{2t}$

$3993 = 3000(1+0.1)^{2t}$

$3993 = 3000(1.01)^{2t}$

$1.331=(1.01)^{2t}$

$\implies t = 14.368\text{ years}$

Hence, After 14.368 years the amount will become Rs.3993 .