Question

What is the present worth of annuity ₹16,000 per year for 3 years, with 10%p.a. rate interest compounded annually.​

Answer 1

Given

• Principal=₹16,000
• Rate%=10%
• Time=3years

To find

• Compound Interest

Step by step explanation

$~~~~~~~~~~~~~\boxed{\pink{ \sf{Compound \: Interest = P \left[\left(1~+~ \frac{R}{100}\right)^n~ –~ 1\right]}}}$

Putting the value in formula

$\sf{Compound \: Interest = 16000 \left[\left(1~+~ \frac{10}{100}\right)^3~ –~ 1\right]}$

$\sf{Compound \: Interest = 16000 \left[\left(~ \frac{100 + 10}{100}\right)^3~ –~ 1\right]}$

$\sf{Compound \: Interest = 16000 \left[\left( \frac{110}{100}\right)^3~ –~ 1\right]}$

$\sf{Compound \: Interest = 16000 \left[\left( \frac{11 \cancel0}{10 \cancel0}\right)^3~ –~ 1\right]}$

$\sf{Compound \: Interest = 16000 \left[ \frac{1331}{1000} ~ –~ 1\right]}$

$\sf{Compound \: Interest = 16000 \left[ \frac{1331 - 1000}{1000}\right]}$

$\sf{Compound \: Interest = 16 \cancel{000} \times \frac{331}{1 \cancel{000}} }$

$\sf{Compound \: Interest = 16 \times 331}$

$\sf{Compound \: Interest =\red{\bold{₹ 5296}}}$

Answer 2

$\sf \pmb{Answer :}$

Given

Principal=₹16,000

Rate%=10%

Time=3years

To find

Compound Interest

Step by step explanation

$~~~~~~~~~~~~~\boxed{\pink{ \sf{Compound \: Interest = P \left[\left(1~+~ \frac{R}{100}\right)^n~ –~ 1\right]}}}$

Putting the value in formula

$\sf{Compound \: Interest = 16000 \left[\left(1~+~ \frac{10}{100}\right)^3~ –~ 1\right]}$

$\sf{Compound \: Interest = 16000 \left[\left(~ \frac{100 + 10}{100}\right)^3~ –~ 1\right]}$

$\sf{Compound \: Interest = 16000 \left[\left( \frac{110}{100}\right)^3~ –~ 1\right]}$

$\sf{Compound \: Interest = 16000 \left[\left( \frac{11 \cancel0}{10 \cancel0}\right)^3~ –~ 1\right]}$

$\sf{Compound \: Interest = 16000 \left[ \frac{1331}{1000} ~ –~ 1\right]}$

$\sf{Compound \: Interest = 16000 \left[ \frac{1331 - 1000}{1000}\right]}$

$\sf{Compound \: Interest = 16 \cancel{000} \times \frac{331}{1 \cancel{000}} }$

$\sf{Compound \: Interest = 16 \times 331}$

$\sf{Compound \: Interest =\red{\bold{₹ 5296}}}$