In the table below, we are given two annuity plans, A and B, and the amount invested into each plan every month. Given this information, determine which of the two investments is an ordinary annuity, and the amount invested over a 12 month period.
| | Jan. | Feb. | Mar. | Apr. | May | Jun. | Jul | Aug | Sept. | Oct. | Nov. | Dec. |
| :---- | :--- | :--- | :--- | :--- | :--- | :--- | :-: | :-: | :---- | :--- | :--- | :--- |
| A | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | |
| B | | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 |
A. Investment A is an ordinary annuity with an annual contribution of $1,100
B. Investment A is an ordinary annuity with an annual contribution of $100
C. Investment B is an ordinary annuity with an annual contribution of $1,100
D. Investment B is an ordinary annuity with an annual contribution of $100
Answer (2)
Calculate the total investment for Plan A: $100 \times 11 = $1100.
Calculate the total investment for Plan B: $100 \times 11 = $1100.
Identify that Plan B is an ordinary annuity because payments start at the end of the period.
Conclude that Investment B is an ordinary annuity with an annual contribution of $1 , 100 .
Explanation
Understanding the Problem We are given two annuity plans, A and B, with monthly investments. We need to determine which plan is an ordinary annuity and the total investment over 12 months. An ordinary annuity is one where payments are made at the end of each period.
Analyzing the Investments Plan A has investments from January to November, each being $100. Plan B has investments from February to December, each being $100.
Calculating Total Investments Let's calculate the total investment for each plan.
For Plan A, the total investment is $100 \times 11 = $1100.
For Plan B, the total investment is $100 \times 11 = $1100.
Identifying the Ordinary Annuity Now, let's determine which plan is an ordinary annuity. Plan A starts payments at the beginning of the period (January), while Plan B starts payments at the end of the first period (February). Therefore, Plan B is an ordinary annuity.
Conclusion Thus, investment B is an ordinary annuity with an annual contribution of $1100.
Examples
Annuities are a common financial tool used for retirement savings. Understanding the difference between an ordinary annuity and an annuity due can help you plan your investments effectively. For example, if you invest $500 per month into an ordinary annuity with a 5% annual interest rate, you can calculate the future value of your investment over a certain period. This knowledge helps in making informed decisions about your financial future and retirement planning.
Investment B is identified as the ordinary annuity because payments start at the end of the period. The total annual contribution for both plans is $1,100, but only Investment B qualifies as an ordinary annuity. Therefore, the chosen answer is C.
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