Question #9a08d

1 Answer
Dec 13, 2016

Answer:

#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#