B.12 Time value of money concepts and calculations Flashcards
(18 cards)
Which of the following best defines the time value of money?
A) The principle that a dollar received today is worth more than a dollar received in the future
B) The principle that a dollar received in the future is worth more than a dollar received today
C) The principle that a dollar received today is worth the same as a dollar received in the future
D) The principle that a dollar received today is worth less than a dollar received in the future
The principle that a dollar received today is worth more than a dollar received in the future
Explanation: The time value of money is the concept that money today is worth more than the same amount of money in the future because of its earning potential. This concept is based on the idea that money can be invested today to earn interest or other returns, so a dollar received today can be worth more than a dollar received in the future.
B.12 Time value of money concepts and calculations
Which of the following is the formula for calculating the future value of an investment?
A) FV = PV x (1 + i)
B) FV = PV x (1 + i)^n
C) PV = FV x (1 + i)
D) PV = FV / (1 + i)^n
FV = PV x (1 + i)^n
Explanation: The future value (FV) of an investment is calculated using the formula FV = PV x (1 + i)^n, where PV is the present value of the investment, i is the interest rate, and n is the number of periods.
B.12 Time value of money concepts and calculations
Which of the following is the formula for calculating the present value of an investment?
A) PV = FV x (1 + i)
B) PV = FV / (1 + i)^n
C) FV = PV x (1 + i)
D) FV = PV x (1 + i)^n
PF =FV / (1 + i)^n
Explanation: The present value (PV) of an investment is calculated using the formula PV = FV / (1 + i)^n, where FV is the future value of the investment, i is the interest rate, and n is the number of periods.
B.12 Time value of money concepts and calculations
An investor is considering two investments, both of which will pay $1,000 in five years. One investment pays interest annually at a rate of 5%, while the other pays interest annually at a rate of 7%. Which investment has a higher present value?
A) The investment that pays 5% interest annually
B) The investment that pays 7% interest annually
C) Both investments have the same present value
D) Insufficient information to determine
The investment that pays 5% interest annually.
Explanation: The present value of an investment is calculated by discounting the future value back to the present using a discount rate, which is equal to the interest rate. Since both investments have the same future value and time horizon, the investment with the lower interest rate will have a higher present value.
B.12 Time value of money concepts and calculations
Which of the following best defines the effective annual rate (EAR)?
A) The annualized interest rate for a loan or investment that includes compound interest
B) The annualized interest rate for a loan or investment that does not include compound interest
C) The interest rate charged on a loan or investment on a monthly basis
D) The interest rate charged on a loan or investment on a daily basis
The annualized interest rate for a loan or investment that includes compound interest
Explanation: The effective annual rate (EAR) is the annual interest rate that includes the effect of compounding interest. It represents the actual rate of return earned or paid on an investment or loan over a year.
B.12 Time value of money concepts and calculations
An investor deposits $5,000 today into a savings account that pays 3% interest annually. How much will the investor have in the account in 10 years?
A) $6,543.21
B) $6,906.63
C) $7,263.24
D) $7,613.40
$7,263.24
Explanation: The future value (FV) of an investment of $5,000 for 10 years at 3% interest annually is calculated using the formula FV = PV x (1 + i)n, where PV = $5,000, i = 3%, and n = 10. FV = $5,000 x (1 + 0.03)10 = $7,263.24.
B.12 Time value of money concepts and calculations
Which of the following is the formula for calculating the present value of an annuity?
A) PV = C / i
B) PV = C x (1 + i)n / i
C) PV = C x (1 - (1 + i)-n) / i
D) PV = C x (1 + i)n
PV = C x (1 - (1 + i)-n) / i
Explanation: The present value (PV) of an annuity is calculated using the formula PV = C x (1 - (1 + i)-n) / i, where C is the periodic payment, i is the interest rate, and n is the number of periods.
B.12 Time value of money concepts and calculations
An investor wants to have $1 million in 20 years for retirement. If the investor can earn 6% interest annually, how much does the investor need to deposit annually to reach this goal?
A) $26,383
B) $27,185
C) $28,290
D) $29,271
$26,383.68
Explanation: The amount of money an investor needs to deposit annually to reach a future value goal can be calculated using the formula PMT = FV x (i / ((1 + i)n - 1)), where PMT is the periodic payment, FV is the future value goal, i is the interest rate, and n is the number of periods.
To solve using the HP 10bII+ enter the following:
Press the Shift (orange key) and then Beg/End to make sure calclator is set to end
1,000,000 and then press FV
20 and then press N
6 and then press I/YR
press PMT
Answer = -27,185 (rounded)
B.12 Time value of money concepts and calculations
Which of the following is the formula for calculating the future value of an annuity?
A) FV = C / i
B) FV = C x (1 + i)^n / i
C) FV = C x (1 - (1 + i)^-n) / i
D) FV = C x (1 + i)^n
FV = C x (1 + i)^n / i
Explanation: The future value (FV) of an annuity is calculated using the formula FV = C x (1 + i)^n / i, where C is the periodic payment, i is the interest rate, and n is the number of periods.
B.12 Time value of money concepts and calculations
An investor wants to have $500,000 in 10 years for a down payment on a house. If the investor can earn 8% interest annually, how much does the investor need to deposit annually to reach this goal?
A) $31,546.16
B) $32,104.23
C) $32,669.75
D) $33,242.07
$32,669.75
Explanation: The amount of money an investor needs to deposit annually to reach a future value goal can be calculated using the formula PMT = FV x (i / ((1 + i)n - 1)), where PMT is the periodic payment, FV is the future value goal, i is the interest rate, and n is the number of periods. In this case, PMT = $500,000 x (0.08 / ((1 + 0.08)10 - 1)) = $32,669.75.
B.12 Time value of money concepts and calculations
Which of the following is the formula for calculating the present value of a perpetuity?
A) PV = C / i
B) PV = C x (1 + i)n / i
C) PV = C / (i - g)
D) PV = C x (1 - (1 + i)-n) / i
PV = C / (i - g)
Explanation: The present value (PV) of a perpetuity is calculated using the formula PV = C / (i - g), where C is the periodic payment, i is the interest rate, and g is the growth rate.
B.12 Time value of money concepts and calculations
An investor aims to have $50,000 saved in 5 years for a child’s college tuition. If the investor can earn an annual interest rate of 4%, how much does the investor need to deposit annually to achieve this goal?
A) $8,500
B) $9,000
C) $9,500
D) $10,000
$9,500
Explanation: In this scenario, we are solving for the annuity given a future value. The formula for the future value of an annuity is FV = PMT × [(1 + r)^n - 1] / r, where PMT is the annuity payment, r is the interest rate per period, and n is the number of periods. We know the future value (FV) is $50,000, the interest rate (r) is 4% or 0.04, and the number of periods (n) is 5. We want to solve for PMT.
Rearranging the formula to solve for PMT gives us: PMT = FV × r / [(1 + r)^n - 1] = $50,000 × 0.04 / [(1 + 0.04)^5 - 1] ≈ $9,500.
B.12 Time value of money concepts and calculations
An investor wants to have $1 million in 30 years for retirement. If the investor can earn 5% interest annually, how much does the investor need to deposit today to reach this goal?
A) $209,135.35
B) $220,347.88
C) $232,196.27
D) $244,715.82
$209,135.35
Explanation: The amount of money an investor needs to deposit today to reach a future value goal can be calculated using the formula PV = FV / (1 + i)n, where PV is the present value, FV is the future value goal, i is the interest rate, and n is the number of periods. In this case, PV = $1,000,000 / (1 + 0.05)30 = $209,135.35.
B.12 Time value of money concepts and calculations
Which of the following statements is true regarding the time value of money?
A) The present value of an investment increases as the interest rate increases
B) The future value of an investment increases as the number of compounding periods increases
C) The present value of an investment decreases as the number of compounding periods increases
D) The future value of an investment decreases as the interest rate decreases
The future value of an investment increases as the number of compounding periods increases
Explanation: The time value of money concept states that the value of money changes over time due to the effects of inflation and interest. The future value of an investment increases as the number of compounding periods increases because each compounding period generates additional interest on the principal plus the previously accumulated interest. The present value of an investment decreases as the interest rate increases because a higher discount rate reduces the value of future cash flows.
B.12 Time value of money concepts and calculations
An investor is planning for retirement and wants to accumulate $500,000 in 20 years. The investor is considering investing $200,000 today at a 6% annual interest rate. Will this investment be sufficient to achieve the investor’s retirement goal?
A) Yes, the investor will achieve her goal with a little extra to spare.
B) No, the investor will not achieve her goal.
C) It depends on the amount of annual contributions made by the investor over the next 20 years.
Yes, the investor will achieve her goal with a little extra to spare.
Explanation: Future value of the $200,000 investment after 20 years:
FV = PV x (1 + r)^n
where PV is the present value or the initial investment amount, r is the annual interest rate, and n is the number of years.
FV = $200,000 x (1 + 0.06)^20
FV = $500,379
So the $200,000 investment at a 6% annual interest rate will grow to $500,379 in 20 years, which is enough to achieve the investor’s goal of accumulating $500,000 in 20 years.
B.12 Time value of money concepts and calculations
A company wants to buy a new machine that costs $50,000. The machine is expected to generate annual net cash flows of $20,000 for the next five years. If the company’s required rate of return is 10%, what is the net present value of the investment?
A) $12,383
B) $15,037
C) $18,342
D) $21,270
$18,342
Explanation: The net present value (NPV) of an investment can be calculated by subtracting the initial investment (in this case, $50,000) from the present value of the expected cash inflows. To calculate the present value of the cash inflows, we can use the formula PV = CF / (1 + r)^n, where CF is the cash flow, r is the required rate of return, and n is the number of periods. Calculating the present value of each year’s cash flow and summing them up, we get:
PV of Year 1 cash flow = $20,000 / (1 + 0.10)^1 = $18,182
PV of Year 2 cash flow = $20,000 / (1 + 0.10)^2 = $16,529
PV of Year 3 cash flow = $20,000 / (1 + 0.10)^3 = $15,026
PV of Year 4 cash flow = $20,000 / (1 + 0.10)^4 = $13,659
PV of Year 5 cash flow = $20,000 / (1 + 0.10)^5 = $12,417
Summing up the present values, we get $75,813. Subtracting the initial investment of $50,000, we get an NPV of $25,813. Therefore, the net present value of the investment is $18,342.
B.12 Time value of money concepts and calculations
An individual wants to have $100,000 in 10 years to purchase a house. Assuming an annual interest rate of 7%, how much money does she need to invest today, if the investment compounds quarterly?
A) $49,617
B) $50,000
C) $51,345
D) $57,203
$51,297
Explanation: To solve this problem using the HP 10bII+ financial calculator, follow these steps:
- Turn On the Calculator: Press ( ON/OFF ).
- Clear Any Previous Work: Press ( [ORANGE SHIFT] ), then ( C ALL ) to reset the calculator.
-
Enter the Given Values:
- ( n ): The total number of compounding periods.
Since it’s compounded quarterly for 10 years: ( n = 4 \times 10 = 40 ).
Enter ( 40 ) and then press ( N ). - ( i \% ): The effective annual interest rate for each period.
Since the annual rate is 7% and it’s compounded quarterly, the quarterly rate is ( 7% \div 4 = 1.75% ).
Enter ( 1.75 ) and then press ( I/Y ). - ( PV ): This is what you want to find, so you’ll leave this alone for now.
- ( PMT ): This is for periodic payments, but since there are no additional contributions, this will be 0. Enter ( 0 ) and then press ( PMT ).
- ( FV ): The desired future value.
Enter ( 100000 ) (or -100000, depending on how the calculator treats cash flow direction) and then press ( FV ).
- ( n ): The total number of compounding periods.
-
Compute the Present Value (PV):
Press ( PV ). This will display the amount she needs to invest today.
The displayed value should be approximately $57,203.07, which is the amount needed to invest today to have $100,000 in 10 years with a 7% annual interest rate compounded quarterly.
B.12 Time value of money concepts and calculations
Sally is self-employed and has decided to save for her retirement in 3 years. She has a consistent Schedule C net income of $237,000, and she contributes $30,000 into a month purchase plan on the last day of each year. How much will his retirement account be worth at his retirement if he achieves 8% growth on his investments?
A) $95,312
B) $97,392
C) $100,182
D) $110,987
$97,392
Explanation
This is a future value of an ordinary annuity problem since Susan contributes at the end of each year.
First, clear the TVM registers.
Press [orange shift key], then [C ALL].
Enter the number of periods (years).
Enter 3, then press [N].
Enter the interest rate.
Enter 8, then press [I/YR].
Enter the payment (annual contribution).
Enter 30000, then press [PMT].
Compute the future value.
Press [FV]. The calculator should display $97,392
B.12 Time value of money concepts and calculations
