Question 62550: 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)2. MV is the maturity value of the CD, r is the interest rate, and t is the number of years left to compound.
Answer by Edwin McCravy(20054)   (Show Source):
You can put this solution on YOUR website! 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)t. MV is the
maturity value of the CD, r is the interest rate, and t is the number of years
left to compound.
MV = P(1 + r)t
Substitute P = 1000, MV = 1210,
t = 2 and solve for r
1210 = 1000(1 + r)2
(1 + r)2 = 1210/1000
(1 + r)2 = 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
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