Question 62550
<pre>Please help me solve this word problem. 
Find the interest rate that would increase your original $1,000 CD, compounded
annually, to $1,210 in two years. The growth formula is MV=P(l+r)<sup>t</sup>. MV is the
maturity value of the CD, r is the interest rate, and t is the number of years
left to compound.
<font size = 5 color = "indigo"><b>

MV = P(1 + r)<sup>t</sup>

Substitute P = 1000, MV = 1210, 
t = 2 and solve for r

1210 = 1000(1 + r)<sup>2</sup>

(1 + r)<sup>2</sup> = 1210/1000

(1 + r)<sup>2</sup> = 121/100

Take square roots of both sides:

1 + r = ±11/10

    r = ±11/10 - 1

Using the +, r = 1/10 = .10 = 10%

Using the - give a negative answer, which we ignore.

So the rate is 10%.

Checking:

At the end of the first year, the 10% interest on 
$1000 is $100. so the new amount at the beginning 
of the second year is $1100.  So at the end of the
second year, the 10% interest on the $1100 is $110. 
So adding that gives $1210.  It checks.

Edwin</pre>