Question

in how many years will a sum of money double al 5% pa compound interest
(a) 15 yrs 3 months (b) 14 yrs 2 months (c) 14 yrs 8 months (d)15yrs 2 months

45.
In how many years a sum of money trebles at 5% pa compound interest payable on half
yearly basis?
(a) 18yrs 7 months (b) 18 yrs 6 months (c) 18 yrs 8 months (d) none of these​

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:

CI = P(1+i)^n

present value को हम 100 मान लेते है

तो double = 200

200=100(1+0.05)^n

200/100=(1+0.05)^n

2=1.05^n. (2=1.5^14.2)

1.5^14.2 =1.5^14.2

n=14.2 years