# Compounded Interest Question

• Sep 18th 2007, 04:16 PM
Norman Smith
Compounded Interest Question
Hello everyone! How are you all doing today? I am having two questions as of now regarding compounded interest.

First one: A small hardware store makes a profit of \$20,000 during its first year. The store owner sets a goal of increasing profits by \$5000 each year for 4 years. Assuming that this goal is met, find the total profit during the first 5 years of business.

Second One: A principal of \$2500 is invested at \$% interest. Find the amount after 20 years if the interest is compounded a. annually, b. semi-annually, c. quarterly, d. monthly, and e. daily

I understand how to do it annually, but I'm not sure about b-e. Thank you all for the help and I'm very grateful for it!
• Sep 19th 2007, 12:23 AM
ticbol
Quote:

Originally Posted by Norman Smith
Hello everyone! How are you all doing today? I am having two questions as of now regarding compounded interest.

First one: A small hardware store makes a profit of \$20,000 during its first year. The store owner sets a goal of increasing profits by \$5000 each year for 4 years. Assuming that this goal is met, find the total profit during the first 5 years of business.

Second One: A principal of \$2500 is invested at \$% interest. Find the amount after 20 years if the interest is compounded a. annually, b. semi-annually, c. quarterly, d. monthly, and e. daily

I understand how to do it annually, but I'm not sure about b-e. Thank you all for the help and I'm very grateful for it!

First one: A small hardware store makes a profit of \$20,000 during its first year. The store owner sets a goal of increasing profits by \$5000 each year for 4 years. Assuming that this goal is met, find the total profit during the first 5 years of business.

1st year, \$20,000.
2nd year, 25,000.
3rd year, 30,000.
4th year, 35,000.
5th year, 40,000.

If you want another way, Arithmetic series way,
a1 = 20,000
d = 5,000
an = a1 +(n-1)d
a5 = 20,000 +(5-1)(5,000) = 40,000
Sn = (n/2)(a1 +an)
S5 = (5/2)(20,000 +40,000) = 5(30,000) = 150,000 dollars.

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Second One: A principal of \$2500 is invested at \$% interest. Find the amount after 20 years if the interest is compounded a. annually, b. semi-annually, c. quarterly, d. monthly, and e. daily

I bet you the \$% interest should be 4% interest.

Compound Interest fpormula:
A = P(1 +i)^n
where
A = amount after n compundings.
P = principal = initial amount, at 0 compoundings.
i = interest at each compounding.
n = number of compoundings.

r = interest rate per year, = 4% = 0.04 here.
So,
annual i = 0.04 per compounding
semi-annual i = 0.04/2 = 0.02 per compounding
quarterly i = 0.04/4 = 0.01 per compounding
monthly i = 0.04/12 = 0.0033333... per compounding
daily i = 0.04/365 = 0.000109589 per compounding

For n,
annual, n = 1 compounding per year
semi-annual = 2 compoundings per year
quarterly = 4 compoundings per year
monthly = 12 compoundings per year
daily = 365 compoundings per year

So, for 5 years:

a) Compounding annually,
A = \$2500(1 +0.04)^(1*5) = \$3041.63

b) Compounding semi-annually,
A = \$2500(1 +0.02)^(2*5) = \$3047.49

c) Compounding quarterly,
A = \$2500(1 +0.01)^(4*5) = \$3050.48

d) Compounding monthly,
A = \$2500(1 +0.0033333...)^(12*5) = \$3052.49

e) Compounding daily,
A = \$2500(1 +0.000109589)^(365*5) = \$3053.47