# Compound interest formula nt

Document Sample

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Compound interest formula: A = A0 ( 1 + n )nt

A is the new value of the investment
A0 is the original amount of the investment
r is the annual interest rate, written as a decimal
n is the number of times the interest is compounded in a year
And t is the length of the investment, in years

Steps: 1) Write down the formula

2) Fill in the missing amounts
Determine the growth rate (______________ ÷ ____________________)

Substitute the values for the original amount, the number of times
compounded, and the time (in years)

3) Calculate

Sample Problems: Find the value of \$3200 invested for 3 years at 6.0% if the interest is
compounded
a) quarterly

b) semi-annually

c) monthly

Solutions
a) A0 = 3200, r = .06, and t = 3. Since the interest is compounded quarterly, n = 4.
This gives us

b) A0 = 3200, r = .06, and t = 3. Since the interest is compounded semi-annually, n = 2.
This gives us
c) A0 = 3200, r = .06, and t = 3. Since the interest is compounded monthly, n = 12.

r
y = C(1 + r)t           y = C(1 – r)t           A  A 0 (1  ) nt
n

1. Mr. Stangeland invested \$1500 in a fund that earns 4%. How much will this
investment be worth in 6 years if the interest is compounded:
a) Quarterly

b) Monthly

2. The town of Algebraville has an inflation rate of 3½ percent. An item today costs \$150.

a) What did it cost 3 years ago? (t = ____)

b) What will it cost when Mr. Stangeland turns 50? (He is currently 35.)
3. Algebra-man is currently taking medication (prescribed) that keeps his brain from
getting too big. The amount of medication in his bloodstream dissipates at a rate of 20%
per hour. At 12:30 p.m., there is approximately 726 mg of the medication in his system.

a) How much was in his system at 9:15 a.m., when he originally took the
medication? (t = ______)

b) How much will remain in his system at 3:15 p.m.? (t = _______)

4. The point (3, 2) is on the graph of y = a • 2x . What is the value of the y-coordinate
when x = 6.

5. (3xy3)4                      6. (ab2c3)–3(a4b3c)4                7. (2m)–5

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