SOLUTION: A certain sum amount to Rs 14400 at 4% simple interest in a period of time in which Rs 9000 amounts to Rs 12150 at 7%. find the sum.

Question 887032: A certain sum amount to Rs 14400 at 4% simple interest in a period of time in which Rs 9000 amounts to Rs 12150 at 7%. find the sum.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the simple interest formula is as follows:
f = p + i * n * p which can be simplified to:
f = p * (1 + i * n)
f is the future value
p is the present value or principal
i is the interest rate per time period
n is the number of time periods.

you are given that 9000 grows at 7% per year for n years and results in 12150.

substitute in the equation of f = p * (1 + i * n) to get:

12150 = 9000 * (1 + .07 * n)

divide both sides of this equation by 9000 to get:

12150 / 9000 = 1 + .07 * n

simplify this to get:

1.35 = 1 + .07 * n

subtract 1 from both sides of the equation to get:

1.35 - 1 = .07 * n

simlify to get:

.35 = .07 * n

divide both sides of the equation by .07 to get:

.35 / .07 = n

solve for n to get:

n = 5

since you now know the value of n, you can substitute in the first equation as follows:

the main equation is still f = p * (1 + i * n)

f = 14400
n = 5
i = .04

equation becomes:

14400 = p * (1 + .04 * 5) which becomes:

14400 = p * (1.2)

divide both sides of this equation by 1.2 to get:

14400 / 1.2 = p

solve for p to get:

p = 12000

the sum that you are looking for is 12000.

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