Question

19. Calculate the present value of an annuity of Rs.1,200 payable quarterly for 3 years @ 12 % p.a
compounded quarterly. Given (1.03)-12 = 0.701380.
a. Rs.11944.80
b. Rs.2524.968
c. Rs.10898.67
d. None​

Answer 1

a. Rs. 11,944.80

The present value is Rs. 11,944.80

Step-by-step explanation:

Given :

Payment amount (R) = Rs 1,200

Interest rate (i) = 12%

Time (n) = 3 years

Payment interval = quarterly

(1.03)⁻¹² = 0.701380

To find :

The present value of an annuity

Solution :

★ we are asked to calculate the present value of the sequence of payment

i = 0.03

n = 12

R = 1,200

Present value =

$\tt{Present \: value = \dfrac{R(1 - (1 + i))}{i}^{-n}}$

$\tt{Present \: value \: = \: \dfrac{1,200(1 - (1 + 0.03))}{0.03}^{ - 12}}$

⇒ $\tt{\dfrac{1,200(1 - 1.03)}{0.03} ^{ - 12}}$

★ According to the question :

(1.03)⁻¹² = 0.701380

So,

⇒ $\tt{\dfrac{1,200(1 - 0.701380)}{0.03}}$

⇒ $\tt{\dfrac{358.344}{0.03}}$

⇒ 11,944.8

Therefore,

a. Rs. 11,944.80

The present value is Rs. 11,944.80

Answer 2

$\huge\fbox \red{✔An} {\colorbox{crimson}{sw}}\fbox\red{er✔}$

Step-by-step explanation:

$a. Rs. 11,944.80</p><p>The present value is Rs. 11,944.80</p><p>Step-by-step explanation:</p><p>Given :</p><p>Payment amount (R) = Rs 1,200</p><p>Interest rate (i) = 12%</p><p>Time (n) = 3 years</p><p>Payment interval = quarterly</p><p>(1.03)⁻¹² = 0.701380</p><p>To find :</p><p>The present value of an annuity</p><p>Solution :</p><p>★ we are asked to calculate the present value of the sequence of payment</p><p></p><p>i = 0.03</p><p>n = 12</p><p>R = 1,200</p><p>Present value = </p><p>[tex]\tt{Present \: value = \dfrac{R(1 - (1 + i))}{i}^{-n}}$

$\tt{Present \: value \: = \: \dfrac{1,200(1 - (1 + 0.03))}{0.03}^{ - 12}}$

⇒ $\tt{\dfrac{1,200(1 - 1.03)}{0.03} ^{ - 12}}$

★ According to the question :

(1.03)⁻¹² = 0.701380

So,

⇒ $\tt{\dfrac{1,200(1 - 0.701380)}{0.03}}$

⇒ $\tt{\dfrac{358.344}{0.03}}$

⇒ 11,944.8

Therefore,

a. Rs. 11,944.80

The present value is Rs. 11,944.80[/tex]