Q: Which of the following is the correct formula for the future value of an ordinary annuity?

$$FVA = C \times \frac{(1 + r)^N - 1}{r}$$

Q: If you want to accumulate $50,000 in 8 years by making equal annual deposits into an account earning 7% interest, which formula would you use to find the required annual deposit?

$$PMT = \frac{FV \times r}{(1 + r)^N - 1}$$

Q: You want to withdraw equal annual amounts for 20 years from your retirement fund, which has a balance of $$423,504.48$$ and earns 9% interest. Which formula would you use to find the annual withdrawal amount?

$$PMT = PV \times \frac{r}{1 - (1 + r$$)^{-N}$$}$$

Question 1

Which of the following best describes the 'time value of money' principle?

Accepted Answer

Money received today is worth more than money received in the future because it can be invested to earn interest.

Question 2

You invest $$1,000 in a savings account that pays 8% interest compounded annually. How much will you have after 3 years? Use the formula FV = PV$$ 	imes (1 + r)^n$.

Accepted Answer

$$1,259.71$$

Question 3

Which rule states that only values at the same point in time can be compared or combined?

Accepted Answer

Rule 1

Question 4

If you want to know the present value of $15,000 to be received in 10 years at a discount rate of 6%, which formula should you use?

Accepted Answer

$$PV = \frac{C}{(1 + r)^n}$$

Question 5

A project costs $$100,000 today and returns 105$$,000 in one year. If the discount rate is 10%, what is the net present value (NPV)?

Accepted Answer

Question 6

Which of the following best describes compounding?

Accepted Answer

The process of moving a value forward in time by earning interest on both the principal and accumulated interest.

Question 7

You lend $$10,000 today and will be repaid in two annual payments of 6$$,000 each. If the discount rate is 5%, what is the present value of the repayments? Use $$PV = \frac{C_1$}{(1 + r)^1$} + \frac{C_2$}{(1 + r)^2$}.$$

Accepted Answer

$$PV = \frac{6,000}{1.05} + \frac{6,000}{(1.05)^2$} = 11$$,337.56

Question 8

Which of the following is the correct formula for the future value of an ordinary annuity?

Accepted Answer

$$FVA = C 	imes \frac{(1 + r)^N - 1}{r}$$

Question 9

If you want to accumulate $50,000 in 8 years by making equal annual deposits into an account earning 7% interest, which formula would you use to find the required annual deposit?

Accepted Answer

$$PMT = \frac{FV 	imes r}{(1 + r)^N - 1}$$

Question 10

A firm receives $$1,000 at the end of each year for 5 years. If the discount rate is 6%, what is the present value of these cash flows? Use PV$$ = \sum_{t=1}^{5} \frac{1,000}{(1.06)^t}$.

Accepted Answer

$$4,212.36$$

Question 11

Which of the following statements about annuities is correct?

Accepted Answer

An annuity is a series of equal cash flows occurring at regular intervals for a finite period.

Question 12

If you invest $$20,000 at 10% interest compounded annually for 10 years, what will be the future value? Use FV = PV$$ 	imes (1 + r)^n$.

Accepted Answer

$$51,874.85$$

Question 13

You are considering an investment that costs $$5,000 today and pays 900 at $$the end of each of the next 7 years. If the discount rate is 10%, should you accept the investment? (Hint: Calculate NPV)

Accepted Answer

Yes, because the NPV is positive.

Question 14

Which of the following best describes discounting?

Accepted Answer

The process of finding the present value of a future cash flow by applying a discount rate.

Question 15

If you receive $$2,000 at the end of each year for 5 years and the interest rate is 10%, what is the total future value at the end of year 5? Use FV = C$$ 	imes \frac{(1 + r)^N - 1}{r}$.

Accepted Answer

$$12,210.20$$

Question 16

A bond will pay $$15,000 in 10 years. If the market interest rate is 6%, what is the bond worth today? Use PV$$ = \frac{15,000}{$$(1.06)^{10}$$}$.

Accepted Answer

$$8,375.92$$

Question 17

Which of the following is NOT a correct application of the three rules of time travel in finance?

Accepted Answer

Adding cash flows that occur at different points in time without adjusting for interest.

Question 18

If you invest $$5,000 per year for 30 years at 9% interest, what will be the future value at the end of 30 years? Use FV = $$PMT 	imes \frac{(1 + r)^N - 1}{r}$.

Accepted Answer

$$681,537.69$$

Question 19

You want to withdraw equal annual amounts for 20 years from your retirement fund, which has a balance of $$423,504.48$$ and earns 9% interest. Which formula would you use to find the annual withdrawal amount?

Accepted Answer

$$PMT = PV 	imes \frac{r}{1 - (1 + r$$)^{-N}$$}$$

Chapter 4: The Time Value of Money – Financial Accounting Study Notes

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