Base and Amount and Rate Help please…?
Joe made a $6,400 investment at the beginning of the year. By the end of the year, the value of the investment had decreased by 8.2%. What was it’s value at the end of the year?
8.2 is the rate
I thought that the amount is followed by the word is and the base of….
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r is the annual rate of interest as a decimal eg.5% means r = 0.05 (here 8.2% in decimal would be 0.082) if the rate is decreasing like in this case we take it negative
n is the number of years you leave it on deposit (here n =1)
A is how much money you’ve accumulated after n years, including interest.
If the interest is compounded once a year:
A = P(1 + r)n
If the interest is compounded q times a year:
A = P(1 + r/q)nq
P is also called base
A = 6400( 1 – 0.082)
A = 6400(0.918)
A = $5875.2
hope this solves ur problem
-8.2% is the rate r of increase (negative because it’s a decrease).
The amount is A, and the relationship between them is:
A = B(1 + r/100)
A = 6400(1 – 8.2/100)
= 6400*(1 – 0.082)
= 6400*0.918
= 5875.20
The value at the year end is $5875.20.
Amount is what you end up with
Rate is the percentage by which your base changes to become the amount.
In this case:
Base = $6400
Rate = 8.2%
Therefore, addition to base = Interest = 8.2% of $6400 = $524.80
Amount = Base + Interest = $6400 + $524.80 = $6924.80
