1. ## 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!

2. 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. Add them all --->$150,000 -----answer.

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