Question

In what time will 5000 amount to 5832, at 16 % per annum , interest being compounded half-yearly?

Answer 1

Answer: Please mark brainliest if it helps.

Let the time be  n half yearlys.

A = 5832

P = 5000

R = 16/2 = 8 percent

5832/5000 =( 1 + 8/100)^n

729/625 = (27/25)^n

27*27/25*25 =  n

2 = n

2 half yearlys

Answer 2

Answer:

2 half - years

Step-by-step explanation:

Given that;

Principal (P) = ₹5000

Amount (A) = ₹5832

Rate (R) = 16 % per annum

             = 8 % per half year.

∴ Amount = ₹ P × { 1 + $\bf (\frac{R}{100})^{n}$}

⇒ ₹ 5832 = ₹ { 5000 × ( 1 + $\sf \frac{8}{100})^{n}$}

⇒ $\frac{5832}{5000}$ = $\sf (\frac{108}{100})^{n}$

⇒ $\frac{729}{625}$ = $\sf (\frac{27}{25})^{n}$

⇒ $(\frac{27}{27})^{2}$ = $\sf (\frac{27}{25})^{n}$

⇒ 2 = n

∴ n = 2 half-years

Hence, the required time is 2 half-years.