Question

a sum of rs 6400 amounts to rs 6724 at 10%p.a. compounded quertely. find the time period​

Answer 1

Answer:

Amount=6569,

Principal=P=6400

RateR==5%,

Time=T=?

Since, we know (for half yearly)

Amount=P(1+  

200

R

​

)  

2T

 

6569=6400(1+5/200)  

2T

 

6400

6569

​

=(  

40

41

​

)  

2T

 

(1.02)  

1

=(1.02)  

2T

 

Comparing the powers when base are same:

1=2T

T=  

2

1

​

 years.

Step-by-step explanation:

Answer 2

Answer:

1/2 years

Step-by-step explanation:

Aₙ = P(1 + I)ⁿ

I = Annual rate of intrest / no: of conversion periods

N = T × no: of conversion periods

Here,

P = 6,400

Aₙ = 6,724

R = 10%

T = ?

Let 'T' be 'n'

Compounded quaterly

Aₙ = P(1 + I)ⁿ

6,724 = 6,400(1 + $\frac{0.1}{4}$)⁴ⁿ

6,724 = 6,400($\frac{4.1}{4}$)⁴ⁿ

6,724 = 6,400(1.025)⁴ⁿ

$\frac{6,724}{6,400}$  = (1.025)⁴ⁿ

1.05078125 = 1.025⁴ⁿ

1.025² = 1.025⁴ⁿ

4n = 2

n = 2/4 = 1/2

VERIFICATION

6400(1 + $\frac{0.1}{4}$)⁴ ˣ ¹/₂ = 6724