Question

a sum of money amounts to rs 1500 in4 years at 5% rate of interest. calculate the principle​

Answer 1

Answer:

Let x be the sum of money and y be the rate of Interest

Using formula for Simple Interest, we have,

x + x * 3 * y / 100 = 1250

i.e. x + 0.03xy = 1250 — (i)

Also, we have,

x + x * 4 * y / 100 = 1500

i.e. x + 0.04xy = 1500 — (ii)

Subtracting, equation (i) from (ii), we get,

0.01xy = 250

i.e. xy = 25000 — (iii)

Substituting equation (iii) in (i), we get,

x + 0.03 * 25000 = 1250

i.e. x + 750 = 1250

i.e. x = 500 — (iv)

Substituting equation (iv) in (iii), we get,

500y = 25000

y = 50

So, the sum is Rs. 500/- and rate of Interest is 50% p.a.

-It is noted that interest is at simple interest thus from above it is clear that one year interest is Rs. 250/- (Rs. 1250/- becomes Rs 1500/- in one year.).

-Thus 3 year interest will be Rs. 750/- as it is simple interest rate.

-Thus Principal amount will be Rs 1250/- less Rs 750/- ie. Rs. 500/-. It is because three year amount is Rs. 1250/- including interest.

-Now interest rate by applying formula will be 50% as under:

Principal = Rs 500

Intrrest one year = Rs 250

Time period = 1 year

250=500xRx1/100

R= 50%

You may verify answer as per your question, Rs 500.00 at 50% interest rate will become Rs 1250 in 3 years and Rs. 1500 in 4 years.

Answer 2

Amount = 1500

Time = 4 years

Rate per annum = 5%

A = P ( 1 + R/ 100 ) ^ t

1500 = P ( 1 + 5/ 100 ) ^ 4

1500 = P ( 100 + 5 ) ^ 4

_____________

100

1500 = P × ( 105 )^4

______

100

1500 = P × 12,15,50,625

_________________

10,00,00,000

1500 × 10,00,00,000 = P

_________________

12,15,50,625

1,50,00,00,00,000 = P

________________________

12,15,50,625

1234.05 = P