Question

Find the present value of Rs 8000 payable at the end of every 3 months for1 and half
years, if

money is worth 8% per annum quarterly.​

Answer 1

Given :- Find the present value of Rs 8000 payable at the end of every 3 months for 1 and half years, if money is worth 8% per annum quarterly.

Solution :-

we know that,

• Present value = (sum each interval / r) * [1 - (1 + r)^(-n)]
• here r is for each Rs and for each payment interval .

so, we have,

• Sum after every 3 months = Rs.8000

r = (8/100) * (1/4) = 0.02 .

n = 6 (for 1.5 years.)

putting values we get,

→ PV = (8000/0.02)[ 1 - (1 + 0.02)^(-6)]

→ PV = 400000[1 - (1.02)^(-6)]

→ PV = 400000[ 1 - 0.89]

→ PV = 400000 * 0.11

→ PV = Rs.44,000 (Ans.)

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Answer 2

Given : Rs 8000 payable at the end of every 3 months for 1 and half years,

money is worth 8% per annum  compounded  quarterly

To Find :

Solution:

We can say that present value is Loan amount and  EQI  ( Equal Quarterly Ins tallment) of Rs 800 to be paid

So present value = Loan amount

P = ?

EQI  = 800

R = 8/4 = 2 %

n = 1 and half years  =  6 Quarters

EQI Formula = [P x (R/100) x (1+(R/100)ⁿ]/[(1+(R/100)ⁿ-1].

=> 8000 = P * (2/100) ( 1 + 2/100)⁶ / (  (1 + 2/100)⁶ - 1)

=>  P = 44,811.45

present value is 44,811.45  Rs

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