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