Question

A certain sum at a certain rate of si amount to rs1125 in 4 yr and rs 1200 in 7 yr find the sum and interest

Answer 1

Answer:

sum = rs 1025

interest = 0.024 per annum

Explanation

Simple Interest Equation (Principal + Interest)

A = P(1 + rt)

Where:

A = Total Accrued Amount (principal + interest)

P = Principal Amount

I = Interest Amount

r = Rate of Interest per year in decimal; r = R/100

R = Rate of Interest per year as a percent; R = r * 100

t = Time Period involved in months or years

Equation 1:

1125 = P(1+r (4))

Equation 2:

1200=P(1+r(7))

Solution

( (1125/P )-1 )/4 = r

putting r in second equation

1200 = P (1+ ( (1125/P )-1 )/4 )* 7)

1200 = P ( 1+ (1125-p)/p)/4) * 7)

1200 = P ( 1+ (1125-p)/4P) * 7)

1200 = P (4p + 7875 -7P ) / 4P

1200 = (7875 - 3P) / 4

4800 = 7875 - 3P

-3075 = - 3P

P = (-3075) / (- 3)

P = 1025

Put value of  P in any equation

1125 = 1025(1+r (4))

1125/1025 = 1 +r (4)

1.0975 = 1 +r (4)

1.0975 -  1 = r (4)

0.0975 = r (4)

r= 0.0975 /4

r = 0.024

Rate of Interest per year as a percent

R = 0.024 *100

R = 2.44

Answer 2

Explanation:

1125 = P(1+r (4))

Equation 2:

1200=P(1+r(7))

Solution

( (1125/P )-1 )/4 = r

4800 = 7875 - 3P

-3075 = - 3P

P = (-3075) / (- 3)

P = 1025

Put value of  P in any equation

1125 = 1025(1+r (4))

1125/1025 = 1 +r (4)

1.0975 = 1 +r (4)

1.0975 -  1 = r (4)

0.0975 = r (4)

r= 0.0975 /4

r = 0.024

Rate of Interest per year as a percent

R = 0.024 *100

R = 2.44