Question #9a08d

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Answer 1 · 2016-12-13T13:13:43

$P = $ 3, 212$ $P= $3,212$

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: $A = P {(1 + r)}^{n}$ $A = P(1+r)^n$
( $A$ $A$ is the total amount of money)

Change the formula to make P the subject.

$P = \frac{A}{{(1 + r)}^{n}}$ $P = A/(1+r)^n$

Make 2 equations from the information which is given:

$P = \frac{4818}{{(1 + r)}^{3}} and P = \frac{7227}{{(1 + r)}^{6}}$ $P = 4818/(1 + r)^3" and "P = 7227/(1+r)^6$

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

Then $\frac{4818}{{(1 + r)}^{3}} = \frac{7227}{{(1 + r)}^{6}}$ $4818/(1+r)^3 = 7227/(1+r)^6$

$:. (1+r)^6/(1+r)^3 = 7227/4818" "larr$ 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= $3,212$