Question

How much will rs 100000 amount to in 3 years, compounded yearly, if the rates of the successive years are 6%, 8% and 10% respectively?

Answer 1

Given :

Principle : ₹100000

Rate of interest(s) : 6%, 8%, 10%

Time : 3 years

To find :

The amount obtained after 3 years.

Solution :

We can find the value of the amount by it's formula.

$\sf \dashrightarrow Amount = Principle \bigg( 1 + \dfrac{R_1}{100} \bigg) \bigg( 1 + \dfrac{R_2}{100} \bigg) \bigg( 1 + \dfrac{R_3}{100} \bigg)$

$\sf \dashrightarrow 100000 \bigg( 1 + \dfrac{6}{100} \bigg) \bigg( 1 + \dfrac{8}{100} \bigg) \bigg( 1 + \dfrac{10}{100} \bigg)$

$\sf \dashrightarrow 100000 \bigg( 1 + \dfrac{3}{50} \bigg) \bigg( 1 + \dfrac{2}{25} \bigg) \bigg( 1 + \dfrac{1}{10} \bigg)$

$\sf \dashrightarrow 100000 \bigg( \dfrac{50 + 3}{50} \bigg) \bigg( \dfrac{25 + 2}{25} \bigg) \bigg( \dfrac{10 + 1}{10} \bigg)$

$\sf \dashrightarrow 100000 \bigg( \dfrac{53}{50} \bigg) \bigg( \dfrac{27}{25} \bigg) \bigg( \dfrac{11}{10} \bigg)$

$\sf \dashrightarrow 2000 \bigg( \dfrac{53}{1} \bigg) \bigg( \dfrac{27}{25} \bigg) \bigg( \dfrac{11}{10} \bigg)$

$\sf \dashrightarrow 80 \bigg( \dfrac{53}{1} \bigg) \bigg( \dfrac{27}{1} \bigg) \bigg( \dfrac{11}{10} \bigg)$

$\sf \dashrightarrow 8 \bigg( \dfrac{53}{1} \bigg) \bigg( \dfrac{27}{1} \bigg) \bigg( \dfrac{11}{1} \bigg)$

$\sf \dashrightarrow 8 (53 \times 27 \times 11)$

$\sf \dashrightarrow 8 (15741)$

$\dashrightarrow$₹$\sf 125928$

Hence, the amount obtained after 3 years is ₹125928.

Answer 2

Step-by-step explanation:

principal=100000

time=3 year

at rate=6%,8%,10%

at first 6%

$si = p \times r \times t \div 100$

$si=100000×6×3÷100$

$si = 1000 \times 6 \times 3$

$si = 18000$

$compounded = simple interest + principle$

$compounded = 100000 + 18000$

$compounded = 118000$

by rate 8%

$si = p \times r \times t \div 100$

$si=100000×8×3÷100$

$si = 1000 \times 8\times 3$

$si = 24000$

$compounded = simple interest + principle$

$compounded=100000+24000$

$compounded = 124000$

by rate 10%

$si = p \times r \times t \div 100$

$si=100000×10×3÷100$

$si = 1000 \times 10\times 3$

$si = 30000$

$compounded = simple interest + principle$

$compounded=100000+30000$

$compounded = 13000$