Use Table 12-2 to find how much should be deposited now at 6% interest, compounded monthly, to yield an annuity payment of $400 at the beginning of each month, for 2 years.
Use Table 12-2 to find how much should be deposited now at 6% interest, compounded monthly, to yield an annuity payment of $400 at the beginning of each month, for 2 years.
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
Problem 1PS
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Question
Use Table 12-2 to find how much should be deposited now at 6% interest, compounded monthly, to yield an annuity payment of $400 at the beginning of each month, for 2 years.
Step 1
The present value of an annuity is the amount needed now so that desired annuity payments may be made in the future. In this scenario annuity payments will be made at the beginning of each month. Thus, this is an annuity due. To find the present value of this annuity, the amount of money that should be deposited in an account now, the interest rate per period must first be found. The interest rate per period is calculated using the nominal, or annual, rate and the number of periods per year as follows.
interest rate per period =
| nominal rate |
| periods per year |
The rate was given to be 6%. Interest is compounded monthly, or 12 times per year. Find the interest rate per period.
| interest rate per period | = |
|
||
| = |
|
|||
| = | % |
The total number of compounding periods will be 1 less than the number of years annuity payments will be made multiplied by the number of compounding periods per year. There are 12 compounding periods per year and payments will be made for 2 years. Find the total number of periods of the annuity.
| total number of annuity periods | = | number of years ✕ number of compounding periods per year − 1 |
| = | 2 ✕ − 1 | |
| = |
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Follow-up Question
We can now use the following formula to find the present value of the account where the annuity payments are $400 each month.
present value = table factor ✕ annuity payment
The table factor was determined to be 21.67568. Before using the above formula, we must add 1 to the table factor since this is an annuity due. Thus, the table factor to use in the formula is
21.67568 + 1 = .
Substitute the values into the formula, rounding the result to the nearest cent.| present value | = | table factor ✕ annuity payment |
| = | ✕ 400 | |
| = | $ |
Therefore, to receive annuity payments of $400 at the beginning of each month for 2 years, the amount that should be deposited now into an account earning 6% interest compounded monthly, to the nearest cent, is
$ .
Solution
by Bartleby ExpertFollow-up Question
The total number of compounding periods will be 1 less than the number of years annuity payments will be made multiplied by the number of compounding periods per year. There are 12 compounding periods per year and payments will be made for 2 years. Find the total number of periods of the annuity.
| total number of annuity periods | = | number of years ✕ number of compounding periods per year − 1 |
| = | 2 ✕ − 1 | |
| = |
Solution
by Bartleby ExpertFollow-up Question
The present value of an annuity is the amount needed now so that desired annuity payments may be made in the future. In this scenario annuity payments will be made at the beginning of each month. Thus, this is an annuity due. To find the present value of this annuity, the amount of money that should be deposited in an account now, the interest rate per period must first be found. The interest rate per period is calculated using the nominal, or annual, rate and the number of periods per year as follows.
interest rate per period =
| nominal rate |
| periods per year |
The rate was given to be 6%. Interest is compounded monthly, or 12 times per year. Find the interest rate per period.
| interest rate per period | = |
|
||
| = |
|
|||
| = | % |
The total number of compounding periods will be 1 less than the number of years annuity payments will be made multiplied by the number of compounding periods per year. There are 12 compounding periods per year and payments will be made for 2 years. Find the total number of periods of the annuity.
| total number of annuity periods | = | number of years ✕ number of compounding periods per year − 1 |
| = | 2 ✕ − 1 | |
| = |
Solution
by Bartleby ExpertKnowledge Booster
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