Which of the following is not equal to .01? 4.
A 102
B 1%
C110
D one one-hundredth
You are considering an annuity that costs $160,000 today. The annuity pays $17,500 a year at an annual interest rate of 7.5 percent. What is the length of the annuity time period?
A.
13 years
B.
14 years
C.
15 years
D.
16 years
E.
17 years
Today, you are retiring. You have a total of $289,416 in your retirement savings. You want to withdraw $2,500 at the beginning of every month, starting today and expect to earn 4.6 percent, compounded monthly. How long will it be until you run out of money?
A.
29.97 years
B.
8.56 years
C.
22.03 years
D.
12.71 years
E.
18.99 years
Your insurance agent is trying to sell you an annuity that costs $50,000 today. By buying this annuity, your agent promises that you will receive payments of $250 a month for the next 20 years. What is the rate of return on this investment?
A.
3.75 percent
B.
2.47 percent
C.
1.88 percent
D.
2.45 percent
E.
3.67 percent
You have been investing $250 a month for the last 13 years. Today, your investment account is worth $73,262. What is your average rate of return on your investments?
A.
8.94 percent
B.
9.23 percent
C.
9.36 percent
D.
9.41 percent
E.
9.78 percent
The Correct Answer and Explanation is :
Here are the answers and explanations for each of the questions:
Question 1: Which of the following is not equal to .01?
Answer: C. 110
Explanation: The decimal representation of .01 is equivalent to:
- A. 102: This is 1/100, which is equal to 0.01 in decimal form.
- B. 1%: 1% is 1 out of 100, which is also equal to 0.01.
- C. 110: This represents one hundred and ten, not a fraction or percentage of 1.
- D. One one-hundredth: This is a direct definition of 0.01.
Therefore, option C is not equal to 0.01.
Question 2: An annuity costs $160,000 today, pays $17,500 annually at 7.5% interest. What is the length of the annuity time period?
Answer: B. 14 years
Explanation: To calculate the length of the annuity time period, we use the present value of an annuity formula:
[
PV = \frac{PMT}{r} \left(1 – (1 + r)^{-n}\right)
]
Where:
- PV is the present value (160,000)
- PMT is the annual payment (17,500)
- r is the interest rate per period (7.5% or 0.075)
- n is the number of periods (years)
Substituting the values into the formula and solving for n gives us 14 years.
Question 3: Withdrawing $2,500 per month for $289,416 at 4.6% interest compounded monthly, how long until money runs out?
Answer: D. 12.71 years
Explanation: This problem involves finding the number of periods (months) for an annuity with monthly withdrawals. Using the formula for the present value of an annuity:
[
PV = \frac{PMT \left(1 – (1 + r)^{-n}\right)}{r}
]
Where:
- PV is the present value (289,416)
- PMT is the withdrawal amount (2,500)
- r is the monthly interest rate (4.6% annually, or 0.003833 per month)
- n is the number of months
Solving for n gives approximately 12.71 years.
Question 4: Annuity costs $50,000, pays $250 per month for 20 years. What is the rate of return?
Answer: D. 2.45 percent
Explanation: This is an annuity problem where we need to find the rate of return. We can use the formula for the present value of an annuity and solve for r:
[
PV = \frac{PMT \left(1 – (1 + r)^{-n}\right)}{r}
]
Where:
- PV is the present value ($50,000)
- PMT is the monthly payment ($250)
- n is the number of periods (240 months)
Solving for r gives approximately 2.45%.
Question 5: Investing $250 per month for 13 years, account worth $73,262. What is the average rate of return?
Answer: B. 9.23 percent
Explanation: We use the future value of an annuity formula to calculate the rate of return:
[
FV = PMT \cdot \frac{(1 + r)^n – 1}{r}
]
Where:
- PMT is the monthly investment ($250)
- FV is the future value ($73,262)
- n is the number of months (13 years * 12 = 156 months)
Solving for r gives approximately 9.23%.
These answers are based on the application of financial formulas for annuities, present and future values, and solving for unknowns like time periods and rates of return.