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Quic 2. Time Value of Money (s Micoosiff fdgel mithilitts nod/quiz/atternpt php...
Sep 21, 2024
To determine whether the present value of a string of CAD 2,000 payments at the end of each year that go on forever at an interest rate of 3.20% is CAD 62,500, we can use the formula for the present value of a perpetuity: PV=Cr PV = \frac{C}{r} where: - PVPV is the present value, - CC is the cash flow per period (CAD 2,000 in this case), - rr is the interest rate (expressed as a decimal, so 3.20% becomes 0.032). Plugging in the values: PV=20000.032=62,500 PV = \frac{2000}{0.032} = 62,500 So, the present value of the payments is indeed CAD 62,500. Therefore, the answer to the quiz question is True. If you have any more questions or need further clarification, feel free to ask!
To determine whether the statement "The EAR of an APR of 8%, compounded semi-annually is 8.24%" is true or false, we can calculate the Effective Annual Rate (EAR) using the formula: EAR=(1+rn)n−1 EAR = \left(1 + \frac{r}{n}\right)^{n} - 1 where: - r r is the nominal interest rate (APR) expressed as a decimal, - n n is the number of compounding periods per year. In this case: - r=0.08 r = 0.08 (8% as a decimal), - n=2 n = 2 (since it is compounded semi-annually). Plugging in the values: EAR=(1+0.082)2−1 EAR = \left(1 + \frac{0.08}{2}\right)^{2} - 1 =(1+0.04)2−1 = \left(1 + 0.04\right)^{2} - 1 =(1.04)2−1 = (1.04)^{2} - 1 =1.0816−1 = 1.0816 - 1 =0.0816 = 0.0816 To express this as a percentage, we multiply by 100: EAR=0.0816×100=8.16% EAR = 0.0816 \times 100 = 8.16\% Since 8.16% is not equal to 8.24%, the statement is False. If you have any more questions or need further clarification, feel free to ask!
To determine whether the statement "The present value of a string of CAD 1,500 payments at the end of the year that go on forever, growing at 2.0% per year at an interest rate of 7.5%, compounded annually is CAD 20,000" is true or false, we can use the formula for the present value of a growing perpetuity: PV=Cr−g PV = \frac{C}{r - g} where: - PVPV is the present value, - CC is the cash flow per period (CAD 1,500 in this case), - rr is the interest rate (7.5% or 0.075), - gg is the growth rate (2.0% or 0.02). Plugging in the values: PV=15000.075−0.02=15000.055≈27,272.73 PV = \frac{1500}{0.075 - 0.02} = \frac{1500}{0.055} \approx 27,272.73 Since CAD 27,272.73 is greater than CAD 20,000, the statement is False. If you have any more questions or need further clarification, feel free to ask!
To determine whether the statement "The present value of a string of CAD 1,500 payments at the end of the year that go on forever, growing at 2.0% per year at an interest rate of 7.5%, compounded annually is CAD 20,000" is true or false, we can use the formula for the present value of a growing perpetuity: PV=Cr−g PV = \frac{C}{r - g} where: - PVPV is the present value, - CC is the cash flow per period (CAD 1,500 in this case), - rr is the interest rate (7.5% or 0.075 as a decimal), - gg is the growth rate (2.0% or 0.02 as a decimal). Plugging in the values: PV=15000.075−0.02=15000.055≈27,272.73 PV = \frac{1500}{0.075 - 0.02} = \frac{1500}{0.055} \approx 27,272.73 Since CAD 27,272.73 is not equal to CAD 20,000, the statement is False. If you have any more questions or need further clarification, feel free to ask!
To determine whether the statement "If a company negotiates a one-year CAD 25,000 discount loan at an interest rate of 5%, compounded monthly, it will receive CAD 23,809.52 today" is true or false, we can calculate the present value of the loan using the formula for the present value of a discount loan. The formula for the present value (PV) of a discount loan is: PV=F(1+r/n)nt PV = \frac{F}{(1 + r/n)^{nt}} where: - F F is the future value (the amount of the loan, CAD 25,000), - r r is the annual interest rate (5% or 0.05), - n n is the number of compounding periods per year (12 for monthly), - t t is the time in years (1 year). Plugging in the values: PV=25000(1+0.05/12)12×1 PV = \frac{25000}{(1 + 0.05/12)^{12 \times 1}} Calculating this gives: PV=25000(1+0.0041667)12≈250001.0511619≈23,809.52 PV = \frac{25000}{(1 + 0.0041667)^{12}} \approx \frac{25000}{1.0511619} \approx 23,809.52 Since the calculated present value is indeed CAD 23,809.52, the statement is True. If you have any more questions or need further clarification, feel free to ask!
To determine whether the statement "CAD 712.50 in interest will be earned over three years on a one-time initial investment of CAD 5,000 at an interest rate of 4.75%, compounded yearly" is true or false, we can calculate the interest earned using the formula for compound interest: A=P(1+r)n A = P(1 + r)^n where: - A A is the amount of money accumulated after n years, including interest. - P P is the principal amount (the initial investment). - r r is the annual interest rate (decimal). - n n is the number of years the money is invested or borrowed. First, we need to convert the interest rate from a percentage to a decimal: r=4.75100=0.0475 r = \frac{4.75}{100} = 0.0475 Now, substituting the values into the formula: A=5000(1+0.0475)3 A = 5000(1 + 0.0475)^3 Calculating this step-by-step: 1. Calculate (1+0.0475)3 (1 + 0.0475)^3 : (1.0475)3≈1.148882 (1.0475)^3 \approx 1.148882 2. Now calculate A A : A≈5000×1.148882≈5744.41 A \approx 5000 \times 1.148882 \approx 5744.41 3. Finally, calculate the interest earned: Interest=A−P=5744.41−5000≈744.41 \text{Interest} = A - P = 5744.41 - 5000 \approx 744.41 Since CAD 744.41 is greater than CAD 712.50, the statement is False. If you have any more questions or need further clarification, feel free to ask!
To determine whether the statement is true or false, we can calculate the interest earned using the simple interest formula: Interest=P×r×t \text{Interest} = P \times r \times t Where: - P P is the principal amount (initial investment), - r r is the annual interest rate (as a decimal), - t t is the time in years. In your case: - P=6,000 P = 6,000 CAD, - r=4.20%=0.042 r = 4.20\% = 0.042 , - t=4 t = 4 years. Now, plug in the values: Interest=6,000×0.042×4 \text{Interest} = 6,000 \times 0.042 \times 4 Calculating that gives: Interest=6,000×0.042×4=1,008 CAD \text{Interest} = 6,000 \times 0.042 \times 4 = 1,008 \text{ CAD} Since the calculated interest of CAD 1,008.00 matches the statement in the question, the answer is True.
Solution by Steps
step 1
To calculate the future value of a series of payments made at the beginning of each year, we use the future value of an annuity due formula: FV=P×((1+r)n−1r)×(1+r) FV = P \times \left( \frac{(1 + r)^n - 1}{r} \right) \times (1 + r) where P=4300 P = 4300 , r=0.0475 r = 0.0475 , and n=5 n = 5
step 2
Plugging in the values into the formula: FV=4300×((1+0.0475)5−10.0475)×(1+0.0475) FV = 4300 \times \left( \frac{(1 + 0.0475)^5 - 1}{0.0475} \right) \times (1 + 0.0475)
step 3
Calculating (1+0.0475)5 (1 + 0.0475)^5 : (1.0475)5≈1.2625 (1.0475)^5 \approx 1.2625
step 4
Now substituting back into the formula: FV=4300×(1.2625−10.0475)×1.0475 FV = 4300 \times \left( \frac{1.2625 - 1}{0.0475} \right) \times 1.0475
step 5
Calculating 0.26250.0475≈5.5263 \frac{0.2625}{0.0475} \approx 5.5263 : FV=4300×5.5263×1.0475 FV = 4300 \times 5.5263 \times 1.0475
step 6
Finally, calculating the future value: FV≈4300×5.5263×1.0475≈23,641.84 FV \approx 4300 \times 5.5263 \times 1.0475 \approx 23,641.84
Answer
A
Key Concept
Future Value of Annuity Due
Explanation
The future value of an annuity due accounts for payments made at the beginning of each period, leading to a higher future value compared to ordinary annuities.
To determine whether the statement "The EAR of an APR of 4%, compounded annually is 4.08%" is true or false, we need to understand how the Effective Annual Rate (EAR) is calculated. When interest is compounded annually, the EAR is equal to the APR. This means that if the APR is 4% and it is compounded annually, the EAR will also be 4%. Therefore, the statement is False. The EAR for an APR of 4% compounded annually is simply 4%, not 4.08%. If you have any more questions or need further clarification, feel free to ask!
To determine whether the present value of a single payment of CAD 75,000 at the end of Year 3 at an interest rate of 5.50%, compounded yearly, is CAD 63,871.02, we can use the present value formula: PV=FV(1+r)n PV = \frac{FV}{(1 + r)^n} Where: - PVPV = Present Value - FVFV = Future Value (CAD 75,000) - rr = interest rate (5.50% or 0.055) - nn = number of years (3) Plugging in the values: PV=75,000(1+0.055)3 PV = \frac{75,000}{(1 + 0.055)^3} Calculating the denominator: (1+0.055)3=(1.055)3≈1.173 (1 + 0.055)^3 = (1.055)^3 \approx 1.173 Now, calculating the present value: PV≈75,0001.173≈63,871.02 PV \approx \frac{75,000}{1.173} \approx 63,871.02 Since the calculated present value matches the statement given in the quiz, the answer is True.
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