Question

P.V. of an annuity of Rs. 80 made at the end of each 6 months forever, if money worth 4% p.a. is compounded semi-annually​

Answer 1

Answer:

Given, A= Rs 500, n=8

Also, r=

100

8

×

4

1

=0.02

∴V=

r

A

×[1−(1+r)

(−n)

]=

0.02

500

×[1−(1.02)

(−8)

]

Now, let x=(1.02)

(−8)

⇒logx=−8log1.02=−8(0.0086)

⇒logx=−0.0688

⇒x=0.8535

⇒V=

0.02

500

×[1−0.8535]= Rs. 3662.50

Thus, the present value of annuity is Rs. 3662.50.

Answer 2

Answer:

The existing price of the annuity is Rs. 4,040.40.

Step-by-step explanation:

The existing price of an annuity is the sum of the discounted values of every payment, the place the cut price fee is the hobby price at which the repayments are being compounded.

In this case, the annuity is Rs. eighty made at the stop of every 6 months, and the activity fee is 4% p.a., compounded semi-annually.

First, we want to locate the semi-annual activity rate, which is half of of the annual activity rate:

Semi-annual pastime charge = (1 + annual hobby rate)^(1/2) - 1

                                                = $(1 + 0.04)^{(1/2)$ - 1

                                                = 0.0198 or 1.98%

Next, we can use the system for the existing cost of an annuity to calculate the current price of the payments:

Present cost of annuity = Payment x [(1 - $(1 + r)^{(-n))$ / r]

where:

Payment = Rs. 80

r = semi-annual pastime charge = 0.0198

n = wide variety of semi-annual durations = infinity (since the annuity is forever)

Substituting the values, we get:

Present fee of annuity = eighty x [(1 - (1 + 0.0198)^(-infinity)) / 0.0198]

                                     = eighty x [1 / 0.0198]

                                     = Rs. 4,040.40

Therefore, the existing price of the annuity is Rs. 4,040.40.

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