Question 1

If the present value annuity factor at 8 percent for 10 years is 6.71, what is the equivalent future value annuity factor?

Accepted Answer

The formula for finding an equivalent future value annuity factor is:
Future Value Annuity Factor = Present Value Annuity Factor * (1+i)^n - 1 / i

Plugging in the given values:
Future Value Annuity Factor = 6.71 * (1+0.08)^10 - 1 / 0.08
Future Value Annuity Factor = 14.486

Therefore, the best choice is B.

Question 2

After retirement, you expect to live for 25 years. You would like to have $75,000 income each year. How much should you have saved in your retirement account to receive this income, if the annual interest rate is 9 percent per year? (Assume that the payments start on the day of your retirement.)

Accepted Answer

To calculate the amount you need in your retirement account, you can use the formula for present value of an annuity:

PV = PMT x [1 - (1 + r)^(-n)]/r

where PV is the present value (or how much you need in your retirement account), PMT is the annual income you want to receive, r is the annual interest rate, and n is the number of years you expect to receive the income (which is 25 in this case).

Plugging in the numbers, we get:

PV = $75,000 x [1 - (1 + 0.09)^(-25)]/0.09 = $802,995.88

Therefore, you would need to have $802,995.88 saved in your retirement account to receive an annual income of $75,000 for 25 years, assuming an annual interest rate of 9 percent.

Question 3

You are considering investing in a retirement fund that requires you to deposit $5,000 per year, and you want to know how much the fund will be worth when you retire. What financial technique should you use to calculate this value?

Accepted Answer

Since the retirement fund requires you to deposit a fixed amount every year, the best financial technique to use would be the future value of an annuity. This will allow you to calculate the total value of the fund at the time of retirement, taking into account the annual deposits and the interest earned on those deposits over time.

Question 4

John House has taken a 20-year, $250,000 mortgage on his house at an interest rate of 6 percent per year. What is the remaining balance (or value)of the mortgage after the payment of the fifth annual installment?

Accepted Answer

The remaining balance after the payment of the fifth annual installment can be calculated using the formula for the remaining balance of an amortizing loan or by using a financial calculator. The calculation involves finding the present value of the remaining 15 payments (20 years total minus 5 years paid) at the original interest rate of 6%. The correct calculation results in a remaining balance of $211,689.53.

Question 5

For $10,000, you can purchase a five-year annuity that will pay $2,504.57 per year for five years. The payments occur at the end of each year. Calculate the effective annual interest rate implied by this arrangement.

Accepted Answer

The effective annual interest rate is 8%. This can be calculated using the formula:Effective annual interest rate = (1 + (nominal annual interest rate / number of compounding periods))^number of compounding periods - 1In this case, the nominal annual interest rate is 5%, the number of compounding periods is 1 (since the payments are made annually), and the number of years is 5. Plugging these values into the formula, we get:Effective annual interest rate = (1 + (0.05 / 1))^1 - 1 = 0.08 = 8%

Question 6

John House has taken a $250,000 mortgage on his house at an interest rate of 6 percent per year. If the mortgage calls for 20 equal, annual payments, what is the amount of each payment?

Accepted Answer

The correct answer is found using the formula for an annuity, which calculates the annual payment required to pay off a loan with interest over a fixed period. Given a principal of $250,000, an annual interest rate of 6% (0.06), and a term of 20 years, the formula gives the annual payment amount, which matches option A, $21,796.14.

Question 7

If the present value annuity factor at 12 percent for five years is 3.6048, what is the equivalent future value annuity factor?

Accepted Answer

To find the equivalent future value annuity factor, we use the formula:
FVAF = (1+r)^n - 1 / r
where r is the interest rate and n is the number of periods.
Therefore, FVAF = (1+0.12)^5 -1 / 0.12 = 6.3529 (rounded to four decimal places).
Thus, the best choice is B.

Question 8

If the present value of $1 received n years from today at an interest rate of r is 0.621, then what is the future value of $1 invested today at an interest rate of r% for n years?

Accepted Answer

The future value of $1 invested today at an interest rate of r% for n years can be found by taking the reciprocal of the present value factor. Since the present value of $1 received n years from today at an interest rate of r is 0.621, the future value is 1 / 0.621 = 1.61.

Question 9

If the future value of $1 invested today at an interest rate of r percent for n years is 9.6463, what is the present value of $1 to be received in n years at r percent interest rate?

Accepted Answer

The future value formula is given by $FV = PV(1+r)^n$, where $FV$ is the future value, $PV$ is the present value, $r$ is the interest rate, and $n$ is the number of years.

In this case, we know that $FV=9.6463$, $PV=1$ (since we are asked to find the present value of $1 to be received in n years), and $n$ and $r$ are unknown.

We can rearrange the formula to solve for $PV$:
$PV = \frac{FV}{(1+r)^n}$

Substituting the given values, we get:
$1 = \frac{9.6463}{(1+r)^n}$

Solving for $1+r$, we get:
$1+r = (9.6463)^{\frac{1}{n}}$

We can then substitute this back into the formula for $PV$:
$PV = \frac{FV}{(1+r)^n} = \frac{1}{(9.6463)^{\frac{1}{n}}}$

Using a calculator or estimating, we get $PV \approx 0.1037$. Therefore, the answer is C.

Question 10

After retirement, you expect to live for 25 years. You would like to have $75,000 income each year. How much should you have saved in your retirement account to receive this income if the annual interest rate is 9 percent per year? (Assume that the payments start one year after your retirement.)

Accepted Answer

To find out how much should be saved in the retirement account, we can use the formula for the present value of an annuity: $PV = PMT \times \left(\frac{1 - (1 + r)^{-n}}{r}\right)$, where PV is the present value (amount needed in the retirement account), PMT is the annual payment ($75,000), r is the annual interest rate (9% or 0.09), and n is the number of years (25). Plugging in the values, we get $PV = 75,000 \times \left(\frac{1 - (1 + 0.09)^{-25}}{0.09}\right)$, which calculates to approximately $736,693.47.

Question 11

For $10,000, you can purchase a five-year annuity that will pay $2,358.65 per year for five years. The payments occur at the beginning of each year. Calculate the effective annual interest rate implied by this arrangement.

Accepted Answer

We can use the formula for present value of an annuity to solve for the effective annual interest rate:

$10,000 = $2,358.65 * \frac{1 - (1+r)^{-5}}{r}

Using trial and error or a financial calculator, we find that the effective annual interest rate (rounded to the nearest whole percent) is approximately 9%. Therefore, the best choice is B.

Question 12

If the present value annuity factor at 10 percent for 10 years is 6.1446, what is the equivalent future value annuity factor?

Accepted Answer

The present value annuity factor (PVAF) is the factor used to calculate the present value of an annuity. The future value annuity factor (FVAF) is the factor used to calculate the future value of an annuity.

FVAF = (1 + r)^(n-1) * PVAF

In this case, r (the interest rate) is 10% and n (the number of years) is also 10.

FVAF = (1 + 0.10)^(10-1) * 6.1446
FVAF = 15.9375

Therefore, the equivalent future value annuity factor is 15.9375, which corresponds to Choice B.

Question 13

If the present value of $1 received n years from today at an interest rate of r is 0.3855, then what is the future value of $1 invested today at an interest rate of r percent for n years?

Accepted Answer

The answer of If the present value of $1 received...

Question 14

If the future value annuity factor at 10 percent and five years is 6.1051, calculate the equivalent present value annuity factor:

Accepted Answer

The equivalent present value annuity factor can be calculated using the formula: PVAF = 1 / (1 + r)^n x [1 - 1 / (1 + r)^n] / r, where r is the interest rate and n is the number of periods. Rearranging this formula, we get: PVAF = (1 - 1 / (1 + r)^n) / r x (1 + r)^-n. Substituting the given values, we get: PVAF = (1 - 1 / 1.1^5) / 0.1 x 1 / 1.1^5 = 3.7908. Therefore, the correct answer is B.

Question 15

If the present value annuity factor is 3.8896, what is the present value annuity factor for an equivalent annuity due if the interest rate is 9 percent?

Accepted Answer

The present value annuity due factor is equal to the present value annuity factor multiplied by (1 + i), where i is the interest rate. Thus, the present value annuity due factor is 3.8896 × (1 + 0.09) = 4.2397. Therefore, the best choice is B.

Question 16

What is the present value of a six-year, $5,000 per year annuity at a discount rate of 10 percent?

Accepted Answer

The present value of an annuity is the sum of the present values of each of the individual payments. The present value of each payment is calculated by dividing the payment by the discount factor, which is 1 / (1 + r)^n, where r is the discount rate and n is the number of periods. In this case, the discount rate is 10% and the number of periods is 6, so the discount factor is 1 / (1 + 0.10)^6 = 0.56447. The present value of each payment is $5,000 / 0.56447 = $8,855.30. The present value of the annuity is the sum of the present values of each of the individual payments, which is $8,855.30 * 6 = $21,776.30.

Question 17

What is the six-year present value annuity factor at an interest rate of 9 percent?

Accepted Answer

The present value annuity factor for 6 years at a 9% interest rate is calculated using the formula for the present value of an annuity. The factor is approximately 4.4859, which matches option B.

Question 18

If the present value annuity factor for 10 years at 10 percent interest rate is 6.1446, what is the present value annuity factor for an equivalent annuity due?

Accepted Answer

The present value annuity factor for an annuity due can be found by multiplying the present value annuity factor for an ordinary annuity by (1 + r), where r is the interest rate. Therefore, for an interest rate of 10 percent (or 0.10), the calculation is 6.1446 * (1 + 0.10) = 6.75906, which rounds to 6.7590.

Question 19

Mr. Hopper expects to retire in 25 years, and he wishes to accumulate $750,000 in his retirement fund by that time. If the interest rate is 10 percent per year, how much should Mr. Hopper put into his retirement fund each year in order to achieve this goal? (Assume that he makes payments at the end of each year.)

Accepted Answer

We can use the formula for the future value of an annuity to solve this problem.

FV = PMT * (((1 + r)^n) - 1) / r

where FV is the future value of the annuity, PMT is the annual payment, r is the interest rate per year, and n is the number of years.

Plugging in the given values, we have:

$750,000 = PMT * (((1 + 0.10)^{25}) - 1) / 0.10

Solving for PMT, we get:

PMT = $7,626.05

Therefore, Mr. Hopper should put $7,626.05 into his retirement fund each year to achieve his goal. The closest option is C, $7,626.05.

Question 20

What is the present value of a $1,000 per year annuity for five years at an interest rate of 12 percent?

Accepted Answer

To find the present value of the annuity, we need to use the annuity formula:

PV = PMT x (1 - 1 / (1 + r)^n) / r

where PV is the present value, PMT is the annual payment, r is the interest rate per period, and n is the number of periods.

In this case, PMT is $1,000, r is 12%, and n is 5. Plugging these values into the formula, we get:

PV = $1,000 x (1 - 1 / (1 + 0.12)^5) / 0.12
PV = $3,604.78

Therefore, the present value of the annuity is $3,604.78. Option B is the only choice that matches this result.

Quiz 2: How to Calculate Present Values