$8000 principal earning 5% compounded annually, after 6 years
1 answer:
Future amount after 6 years will be: $10720.76
Step-by-step explanation:
Principal = $8000
Interest= 5% compounded annually
Time = 6 years
We need to find A (future amount)
The formula used is:
A= Future amount
P= Principal amount
r= interest rate
n= no of times interest is applied
t= time
Putting values and finding A
P=8000. r=0.05, n=1, t=6
So, Future amount after 6 years will be: $10720.76
Keywords: Compound Interest
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<h3>Answer:</h3>
- using y = x, the error is about 0.1812
- using y = (x -π/4 +1)/√2, the error is about 0.02620
The actual value of sin(π/3) is (√3)/2 ≈ 0.86602540.
If the sine function is approximated by y=x (no error at x = 0), then the error at x=π/3 is ...
... x -sin(x) @ x=π/3
... π/3 -(√3)/2 ≈ 0.18117215 ≈ 0.1812
You know right away this is a bad approximation, because the approximate value is π/3 ≈ 1.04719755, a value greater than 1. The range of the sine function is [-1, 1] so there will be no values greater than 1.
___
If the sine function is approximated by y=(x+1-π/4)/√2 (no error at x=π/4), then the error at x=π/3 is ...
... (x+1-π/4)/√2 -sin(x) @ x=π/3
... (π/12 +1)/√2 -(√3)/2 ≈ 0.026201500 ≈ 0.02620