chapter 7 lesson 8 -10 simple interest\nlesson 10 (sect 7.4) present valuep = s/(1+rt)\nproblem a\nexample…

chapter 7 lesson 8 -10 simple interest\nlesson 10 (sect 7.4) present valuep = s/(1+rt)\nproblem a\nexample 1\ndetermine the deposit that must be made to earn $550.27 in 255 days at 11% simple interest.\nexample 2 change of wording\ndetermine the deposit that must be made to amount to $550.27 in 255 days at 11% simple interest.\nproblem b\nexercise 7.4 page 285\n#2 what amount of money will accumulate to $480.57 in 93 days at 4.6%?\nproblem c\n#4 compute the present value of a debt of $708.13, eighty days before it is due if money is worth 5.3%.\nproblem d\n#6 the annual deerfield golf club membership fees of $1750 are due on march 1, 2022. club management offers a reduction of membership fees of 18.9% p.a. to members who pay by september 1, 2021. how much must a member pay on september 1, 2021 if she chooses to take advantage of the club management’s offer?\nproblem e\n#8 on march 15, 2024, ben bought a government - guaranteed short - term investment maturing on september 12, 2024. how much did ben pay for the investment if he will receive $10,000 on september 12, 2024, and interest is 2.06%?\nproblem f present value comparison\nyou have a choice of receiving $10,000 now or $11,000 later. in terms of today’s dollar, which choice is better and by how much?

chapter 7 lesson 8 -10 simple interest\nlesson 10 (sect 7.4) present valuep = s/(1+rt)\nproblem a\nexample 1\ndetermine the deposit that must be made to earn $550.27 in 255 days at 11% simple interest.\nexample 2 change of wording\ndetermine the deposit that must be made to amount to $550.27 in 255 days at 11% simple interest.\nproblem b\nexercise 7.4 page 285\n#2 what amount of money will accumulate to $480.57 in 93 days at 4.6%?\nproblem c\n#4 compute the present value of a debt of $708.13, eighty days before it is due if money is worth 5.3%.\nproblem d\n#6 the annual deerfield golf club membership fees of $1750 are due on march 1, 2022. club management offers a reduction of membership fees of 18.9% p.a. to members who pay by september 1, 2021. how much must a member pay on september 1, 2021 if she chooses to take advantage of the club management’s offer?\nproblem e\n#8 on march 15, 2024, ben bought a government - guaranteed short - term investment maturing on september 12, 2024. how much did ben pay for the investment if he will receive $10,000 on september 12, 2024, and interest is 2.06%?\nproblem f present value comparison\nyou have a choice of receiving $10,000 now or $11,000 later. in terms of today’s dollar, which choice is better and by how much?

Answer

Explanation:

Step1: Identify the present - value formula

The formula for present value is $P=\frac{S}{1 + rt}$, where $P$ is the present value, $S$ is the future value, $r$ is the annual interest rate (in decimal form), and $t$ is the time in years.

Step2: Solve Problem B

First, convert the time $t$ from days to years. $t=\frac{93}{365}$ years and $r = 0.046$, $S=480.57$. Substitute into the formula: $P=\frac{480.57}{1+0.046\times\frac{93}{365}}$ $P=\frac{480.57}{1 + 0.046\times0.254795}$ $P=\frac{480.57}{1+0.01172057}$ $P=\frac{480.57}{1.01172057}\approx475.00$

Step3: Solve Problem C

Convert the time $t=\frac{80}{365}$ years, $r = 0.053$, $S = 708.13$. Substitute into the formula: $P=\frac{708.13}{1+0.053\times\frac{80}{365}}$ $P=\frac{708.13}{1+0.053\times0.219178}$ $P=\frac{708.13}{1 + 0.01161643}$ $P=\frac{708.13}{1.01161643}\approx699.90$

Step4: Solve Problem D

The time from September 1, 2021 to March 1, 2022 is $t=\frac{181}{365}$ years, $r=0.189$, $S = 1750$. Substitute into the formula: $P=\frac{1750}{1+0.189\times\frac{181}{365}}$ $P=\frac{1750}{1+0.189\times0.49589}$ $P=\frac{1750}{1+0.09372321}$ $P=\frac{1750}{1.09372321}\approx1600.00$

Step5: Solve Problem E

The time from March 15, 2024 to September 12, 2024: Number of days from March 15 to March 31 is $31 - 15=16$ days. April has 30 days, May has 31 days, June has 30 days, July has 31 days, August has 31 days, and September has 12 days. $t=\frac{16 + 30+31+30+31+31+12}{365}=\frac{181}{365}$ years, $r = 0.0206$, $S = 10000$. Substitute into the formula: $P=\frac{10000}{1+0.0206\times\frac{181}{365}}$ $P=\frac{10000}{1+0.0206\times0.49589}$ $P=\frac{10000}{1+0.01021533}$ $P=\frac{10000}{1.01021533}\approx9900.85$

Step6: Solve Problem F

Assume an interest - free situation for the comparison. The present value of $10000$ received now is $P_1 = 10000$. The present value of $11000$ received later (assuming no interest rate information, we just consider the time - value concept in a simple way) is $P_2 = 11000$ in the future. In terms of present - day value, if we assume no interest rate, the difference is $11000-10000 = 1000$. But if we consider a non - zero interest rate, we would need to know the time until the $11000$ is received and the interest rate to calculate the present value of $11000$ accurately. For a simple comparison without interest rate and time information, receiving $11000$ later is better by $1000$ in future - value terms.

Answer:

Problem B: $$475.00$ Problem C: $$699.90$ Problem D: $$1600.00$ Problem E: $$9900.85$ Problem F: Receiving $$11000$ later is better by $$1000$ (in a simple non - interest rate adjusted comparison)