Concept explainers
(a)
The amount that is invested today in n years will be
(a)
Answer to Problem 65RE
The value is
Explanation of Solution
Given information:
The favourite school or charity $1000 a year forever. It is known as perpetuity. The earning is 8% annually on the money, hence the payment is worth
Formula used:
Substitution method is used.
Calculation:
Let the amount be invest be x after n years the amount of money be earned=$1000 Also, earning from the money is 8% of the total money every year.
Therefore, after n years,
Conclusion:
The value is
(b)
The series that gives the amount that is to be invested to cover the payments in perpetuity.
(b)
Answer to Problem 65RE
The total amount invested to cover all the payment is
Explanation of Solution
Formula used:
Addition is done.
Calculation:
Assume that the first payment goes to charity at the end of the first year. Therefore, total amount invested to cover all the payment is,
Conclusion:
The total amount invested to cover all the payment is
(c)
The series get converges or not.
(c)
Answer to Problem 65RE
The series converges and the sum is $12,500.
Explanation of Solution
Given information:
The given series is
Formula used:
The ratio is
Calculation:
If the sequence of partial sum has a limit as
The sum of the infinite geometric series whose ratio is
Therefore, sum of the series is
This means that $12,500 should be invested today in order to complete fund the perpetuity forever.
Conclusion:
The sum is $12,500.
Chapter 10 Solutions
Calculus: Graphical, Numerical, Algebraic
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