Question

sunayana borrowed a sum of rs 12,500 at 12% per annum simple interest for 1 year and 6 months and lent to bishwant at the same rate of compound interest compounded half yearly for the same interval of time. how much profit did she make?​

Answer 1

Answer:

Rs 66

Step-by-step explanation:

FV₁=PV.(1+r·t)

Pv=12500, r=0.12,t=1.5

FV₁=12500 x (1+0·12x1.5)=14750  ( simple interest)

FV₂=PV(1+r)^n

PV=12800   r = 0.12    n= 1.5

FV₂=12800x(1+0.12)^1.5

=14816  (compound interest)

FV₂-FV₁=14816-14780=66

Answer 2

Answer:  Rs 137.70

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Explanation:

6 months = 1/2 year = 0.5 year

1 year, 6 months = 1 yr + 0.5 yr = 1.5 years

Sunayana borrows Rs 12,500 at 12% annual interest for 1.5 years

The amount simple interest she must pay back is

i = p*r*t

i = 12500*0.12*1.5

i = 2,250

The amount of simple interest she must pay back is Rs 2,250 which is on top of the principal Rs 12,500

The total amount she must pay back is p+i = 12,500+2,250 = 14,750

Let x = 14,750 so we can use it later.

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She lends that Rs 12,500 to her friend and this amount is compounded half yearly, aka semiannually. So we'll use n = 2.

The amount Bishwant must pay back to her is

A = p*(1+r/n)^(n*t)

A = 12500*(1+0.12/2)^(2*1.5)

A = 14,887.70

Let y = 14,887.70 so we can use it later.

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Subtract the values of y and x to get the profit she makes

profit = revenue - costs

profit = y - x

profit = 14,887.70 - 14,750

profit = 137.70

The profit is Rs 137.70