Question

In how many years will a sum of 30,000 amount to 31.827 at the rate of 6% per annum compouded semi annually
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Answer 1

In 1 years will sum of 30,000 amount to 31,827

Step-by-step explanation:

Amount, A = Rs 31,827/-

Sum, P = 30,000

Time, t = ? years

Rate, r = 0.06 Per annum

Compounded semi-annually, n = 2

So,

$A=P(1+\frac{r}{n})^{nt}$

$31827=30000(1+\dfrac{0.06}{2})^{2t}$

$(1+\dfrac{0.06}{2})^{2t}=\dfrac{31827}{30000}$

$(1.03)^{2t}=1.0609$

Apply log both sides

$2t\log 1.03=\log 1.0609$

$2t=2$

$t=1$

#BAL

Answer 2

Answer:

P=30,000

A= 31827

R=6%

N=?

A=P(1+R/2*100)2n

31827=30000(1+6/2*100) 6 cancel by 3 and 2 by 1

30000 = (1+3/100)=31827

(1+3/100)2n = 31827/ 30000 31827 is cancelled by 10609 and 30000 is cancelled by 10000

(103/100)2n = (103)/(100)2 = (103/100)

2n=2

n=2/2=1

n=1 year

therefore 1 year is a answer

thank you i hope it helped you