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put this solution on YOUR website!# 2
Start with the given formula
Plug in
Distribute
So at the end of the first year, he has
dollars in the account
Since "At the beginning of the second year, an additional $3500 is invested", this means that we simply add 3,500 to the amount
to get
So at the beginning of the second year, he invests
dollars
So this time
Go back to the given formula
Plug in
(this is the amount that is in the account after the second year) and
FOIL
Subtract 15,569.75 from both sides
Combine like terms
Multiply
every term by the 100 to clear the decimals.
Notice we have a quadratic equation in the form of
where
,
, and
Let's use the quadratic formula to solve for r
Start with the quadratic formula
Plug in
,
, and
Square
to get
.
Multiply
to get
Rewrite
as
Add
to
to get
Multiply
and
to get
.
Take the square root of
to get
.
or
Break up the expression.
or
Combine like terms.
or
Simplify.
So the possible answers are
or
which approximate to
or
However, since a negative interest rate doesn't make much sense, this means that the only solution is
which is the percentage 8.5%
-----------------------------------------------------
Answer:
So the interest rate is 8.5%
