If the sequence 2, 4, 6, 10, 16, ... were to follow the same pattern as the Fibonacci sequence, what are the next three terms?
1 answer:
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Answer:
a) 8.16%
b) $65,762.50
c) $39,701.07
Step-by-step explanation:
Given:
15 years ago, Initial investment = $12500
5 years ago, Investment = $20000
Nominal interest = 8% semi annually for first 10 years
Interest2= 6.5% compunded annually for last five years
a) for the effective annual interest rate (EAR) in the first 10 years, let's use the formula:
[1+(nominal interest rate/number of compounding periods)]^ number of compounding periods-1
= 1.0816 - 1
= 0.0816
= 8.16%
The effective annual interesting rate, EAR = 8.16 %
b) To find the amount in my account today.
Let's first find the amount for $12500 for 10 years compounded semi annually
= 12,500 +( 12,500 * 8.160% * 10)
= $ 22,700
Let's also find the amount for $32,500($12,500+$20,000) for 5 Years compoundeed annually
$32,500 + ($32,500 * 6.5% *5)
= $ 43,062.50
Money in account today will be:
$22,700 + $43,062.50
= $65,762.50
c) Let's the amount I should have invested to be X
For first 10 years at 8.160%, we have:
Interest Amount = ( X * 8.160% * 10 ) = 0.8160 X
For next 5 years at 6.5%, we have:
Interest Amount = (X * 6.5% * 5) = 0.325 X
Therefore the total money at the end of 15 Years = 85000
0.8160X + 0.3250X + X = $85,000
= 2.141X = $85,000
X = 85,000/2.141
X = 39,701.074 ≈ $39,700
If I wish to have $85,000 now, I should have invested $39,700 15 years ago
The table is
x | 4 | 8 | 12
y | 1 | 2 | 3
The question is not understandable. The well-formatted question is
Complete the table for the given rule
Rule:
Table:
x | 4 | 8 | 12
y | ? | ? | ?
Evaluation of an algebraic expression when a specified integer is used to replace a variable is known as evaluating the expression. We use the provided number to replace the expression's variable before applying the sequence of operations to simplify the expression.
For instance
On evaluation of y= x+7 when x=3, and x=12
we get y(3) = 3 + 7 = 10 and y(12) = 12 + 7 = 19
The given equation is
So, the table is
x | 4 | 8 | 12
y | 1 | 2 | 3
Learn more about evaluation here-
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