
a.
To find: The annual interest rate.
The annual interest rate is 8%.
Given information:
The function describes the present value of a certain annuity, where x is time in months:
Concept used:
The present value PV of an annuity consisting of n equal payments of R dollars earning an interest rate i per period (payment interval) is
Explanation:
The annual interest rate is determined by the term 0.08 i.e., 8%.
b.
To find: The number of payments per year.
There are 12 payments per year.
Given information:
The function describes the present value of a certain annuity, where x is time in months:
Concept used:
The present value PV of an annuity consisting of n equal payments of R dollars earning an interest rate i per period (payment interval) is
Explanation:
Here, in the given equation “12” determines the number of payments per year.
c.
To find: The amount of each payment.
The amount of each payment is $200.
Given information:
The function describes the present value of a certain annuity, where x is time in months:
Concept used:
The present value PV of an annuity consisting of n equal payments of R dollars earning an interest rate i per period (payment interval) is
Explanation:
On comparing the formula,
i.e., The amount of each payment is $200.
d.
To compute: The present value of the annuity paying $200 monthly after 20 years.
The present value of the annuity is $23,910.86.
Given information:
The function describes the present value of a certain annuity, where x is time in months:
Concept used:
The present value PV of an annuity consisting of n equal payments of R dollars earning an interest rate i per period (payment interval) is
Explanation:
Substitute
The present value of the annuity paying $200 monthly after 20 years is $23,910.86.
e.
To graph: The present value function for x in the interval 0 to 20 years.
The graph of the present value function for x in the interval 0 to 20 years is shown.
Given information:
The function describes the present value of a certain annuity, where x is time in months:
Concept used:
The present value PV of an annuity consisting of n equal payments of R dollars earning an interest rate i per period (payment interval) is
Explanation:
By using graphing calculator, plot the given expression.
f.
To explain: The amount $23,910.86 is much less than the total of all 240 monthly payments of $200, which is $4800.
$23,910.86 is the present value of the annuity paying $200 monthly after 20 years.
Its future value will be much higher than $48,000.
$23,910.86 as present value would be a better option for now.
Given information:
The function describes the present value of a certain annuity, where x is time in months:
Concept used:
The present value PV of an annuity consisting of n equal payments of R dollars earning an interest rate i per period (payment interval) is
Explanation:
$23,910.86 is the present value of the annuity paying $200 monthly after 20 years.
Its future value will be much higher than $48,000.
Thus, $23,910.86 as present value would be a better option for now.
Chapter 3 Solutions
EBK PRECALCULUS:GRAPHICAL,...-NASTA ED.
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