Question

Question #9a08d

Answer 1

`P= $3,212`

Explanation:

There are two quantities which we do not know, and they are the starting amount of money, called P, and the rate of interest called r.

We have 2 different pieces of information involving P and r.

For compound interest: `A = P(1+r)^n`
(`A` is the total amount of money)

Change the formula to make P the subject.

`P = A/(1+r)^n`

Make 2 equations from the information which is given:

`P = 4818/(1 + r)^3" and "P = 7227/(1+r)^6`

The sum of money, P, is the same, therefore `P=P`

Then `4818/(1+r)^3 = 7227/(1+r)^6`

`:. (1+r)^6/(1+r)^3 = 7227/4818" "larr` simplify each side

`(1+r)^3 = 3/2 = 1.5`

It is not necessary to find the value of r, so we can just substitute into the first equation:

`P = 4818/(1 + r)^3" "rarr" "P = 4818/1.5`

`P= $3,212`