Question

A certain sum amounts to Rs 77,000 in 5 years and to Rs 68,200 in 3 years, under simple interest. If the rate of interest is increased by 2%, then in how many years will it double itself?​

Answer 1

In 10 years the money would double itself.

Step-by-step explanation:

In 5 years the maturity of a certain amount  = ₹ 77,000

In 3 years the maturity of a certain amount = ₹ 68,200

In two years the interest amount would be = 77,000 - 68,200

                                                                       = 8,800

In one year the interest amount would be =  $\frac{8800}{2}=4400$

In one year the amount of interest = 4400

In 5 years the amount of interest = 4400 × 5 = ₹ 22,000

Principal amount (P) = maturity amount (A) - interest (I)

P = 77,000 - 22,000 = 55,000

The principal amount was ₹ 55,000

Now we will calculate the rate of interest by the formula :

$r=(\frac{1}{t})(\frac{A}{P}-1)$

$=(\frac{1}{5} )(\frac{77000}{55000}-1 )$

$=\frac{7}{25}+\frac{-1}{5}$

$=\frac{2}{25}=0.08$

= 8%

Now f the rate of interest is increased by 2% then rate of interest will be

= 8% + 2% = 10%

Now we have to calculate the time to calculate the future amount would be double itself.

Formula for time in simple interest :

$t=(\frac{1}{r})(\frac{A}{P}-1 )$

where, r = 10% = 0.10

           A = double of principal amount = 55000 × 2 = ₹ 1,10,000

           P = principal amount = ₹ 55,000

Now put the values into formula

$t=(\frac{1}{0.10})(\frac{110000}{55000}-1 )$

t = 20 - 10

t = 10 years

In 10 years the money would double itself.

Learn more about compound interest : https://brainly.in/question/9454580

Answer 2

Step-by-step explanation:

Step-by-step explanation:

Required Formulas:

Simple Interest = Amount – Principal =

Step 1:

Let the sum of money be denoted as “P” and the rate of interest be denoted as “R”%.

It is given that the sum amounts to Rs. 77000 in 5 years, so using the formula, we get

77000 – P =

⇒ 77000 - P =

⇒ 1540000 - 20P = PR ....... (i)

Step 2:

Also given, the sum amounts to Rs. 68200 in 3 years, so using the formula, we get

68200 - P =

⇒ 6820000 - 100P = 3PR

⇒ 6820000 - 100P = 3 [1540000 - 20P] ........ [substituting from (i)]

⇒ 6820000 - 100P = 4620000 - 60P

⇒ 40P = 6820000 - 4620000

⇒ 40P = 2200000

⇒ P = Rs. 55000

Substituting the value of P in eq. (i), we get

1540000 - (20 * 55000) = 55000 * R

⇒ 1540000 - 110000 = 55000 * R

⇒ R = 440000/55000

⇒ R = 8%

Step 3:

It is given that the sum of money will get doubled

i.e., ∵ P = Rs. 55000 then Amount = 55000 * 2 = Rs. 110000

∴ Simple Interest = 110000 - 55000 = Rs. 55000

The rate of interest is increased by 2% i.e., now the rate of interest becomes = 2 + 8 = 10%

Let the time period for this case be denoted as "T" years.

Therefore,

55000 =

⇒ T = 10