Concept explainers
(a)
Show that if interest is compounded daily , that is , n is very large, the Compound Interest Formula is
(a)
Explanation of Solution
Formula Used:
Calculation:
Compound Interest Formula is :
where
P= Principal
r = annual interest rate in decimal
t = time in years
A = Final amount after t years
n = number of times the interest is compounded in a year
Since n is very large , apply limit on each side:
Hence proved.
(b)
Find the amount of money that you would have after 1 year if you invest $1000 at 6% interest compounded daily.
(b)
Answer to Problem 51WE
$1,061.8
Explanation of Solution
Calculation:
From part(a) , we have the Compound Interest Formula , if the interest is compounded daily:
where
P= Principal = 1000
r = annual interest rate in decimal = 6% = 0.06
t = time in years = 1 year
A = Final amount after t years
Substitute the values and solve for A :
So, the amount after 1 year is about $1,061.8
Chapter 10 Solutions
Algebra and Trigonometry: Structure and Method, Book 2
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