Question

In what time will a sum of money double itself at 5% pa. C.I.​

Answer 1

Answer:

(1) (b) Time = 14 years 2 months

(2) (d) Time = None of these.

Step-by-step explanation:

In the question,

1).

Let, us say the principal amount, P = x

We want the amount to be double, A = 2x

Rate of interest, r = 5% per annum

So,

We know that the Compound Interest is given by,

CI=P(1+\frac{r}{100})^{t}-P\\2x=x(1+\frac{5}{100})^{t}\\2=(1.05)^{t}\\So,\\t=14.265\ years

So, the time taken is 14 years and 2 months.

2).

In the question,

Let us say the Principal amount is, P = x

We want the triple the amount, A = 3x

Rate of interest, r = 5% compounded half yearly

So,

Rate, r = 5/2 = 2.5%

So,

3x=x(1+\frac{2.5}{100})^{2t}\\3=(1.025)^{2t}\\log(3)=2t\times log(1.025)\\2t=44.579\\t=22.289\ years

Therefore, the time taken is 22 years and 3 months.

Answer 2

Answer:

let the principal be rupees 100

amount = rupees 200

so the interest will be 200-100= 100 rupees

time = si × 100 / R × P 100× 100 / 5 × 100 = 20 years .