Question

A certain sum of money is invested for a certain number of years at simple interest rate. If the sum is
invested at a rate 8%, then it grows to $180 and if the same sum of money is invested at a rate of 4%,
then it grows to $120. For how many years was the sum invested?​

Answer 1

Answer:

: A sum of money invested for a certain number of years at 8% p.a. simple interest grows to Rs.180. The same sum of money invested for the same number of years at 4% p.a. simple interest grows to Rs.120. For how many years was the sum invested?

For SIMPLE interest, the total value (T) is determined as T= Principle x (1 + (number of periods)(interest Rate)) T =P(1+(n)(R))

For the 8% scenario we have: 180=P(1+(n)(.08)) 180= P(1+.08n)

For the 4% scenario we have: 120=P(1+(n)(.04)) 120= P(1+.04n)

Solving the latter for P in terms of n yields: P= 120÷(1+.04n) and P= 180÷(1+.08n)

So, 120÷(1+.04n)=180÷(1+.08n)

Separate the unknown parts to yield:

(1+.08n)÷(1+.04n) =180÷120 = 1.5

Multiply both sides by (1+.04n) to get:

(1+.08n)= 1.5 + .06n

Combine terms to get

0.02n = .5

n= .5÷.02 = 25 years

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