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8) Mr: Jonathan who is a vintage car collector negotiated to buy Ms_ Alisha s 1920 Ford Model-T for a price of S60,000. Based on the advice of her tax consultant; M...

Question

8) Mr: Jonathan who is a vintage car collector negotiated to buy Ms_ Alisha s 1920 Ford Model-T for a price of S60,000. Based on the advice of her tax consultant; Ms_ Alysha Agreed with Mr: Jonathan that payment should be effected at the end of 10 years when Ms. Alisha hopes to fall in to lower tax bracket after retirement. Mr: Jonathan therefore thought it prudent to deposit money annually in a sinking fund that will accumulate S60,000 at the time he will be paying Ms_ Alisha: Assuming this sin

8) Mr: Jonathan who is a vintage car collector negotiated to buy Ms_ Alisha s 1920 Ford Model-T for a price of S60,000. Based on the advice of her tax consultant; Ms_ Alysha Agreed with Mr: Jonathan that payment should be effected at the end of 10 years when Ms. Alisha hopes to fall in to lower tax bracket after retirement. Mr: Jonathan therefore thought it prudent to deposit money annually in a sinking fund that will accumulate S60,000 at the time he will be paying Ms_ Alisha: Assuming this sinking fund will earn 6% interest compounded quarterly; calculate the regular payments that Mr: Jonathan will be making into the account each time



Answers

Buying a Car Amanda Perdaris wants to have a $\$ 20,000$ down payment when she buys a new car in 6 years. How much money must she deposit at the end of each quarter in an account paying 3.2$\%$ compounded quarterly so that she will have the down payment she desires?

Are. They agreed to pay four thousand dollars for the stamp. But you gotta pay interestingly annually for five years. You're gonna pay the four thousand dollars after five years. So what is your semi annual interest payment? Will the total amount of interest you're going to pay on this four thousand dollars? Well, you're going to pay six percent interest. Hey, annually for five years, which is going to be twelve hundred dollars. But then you're breaking that up into semi annual payments. Two over five years. So that's going to tent of payments, which divide that two hundred dollars. Ten. I don't get one hundred twenty dollars. Is the amount to pay an interest every twice a year in this case. Okay, so you still gotta pay the four thousand dollars. So you're gonna put money in account that pays eight percent interest, compounded annually. So doing it now. How much do you need A deposit at the end of every year? My interest rate is your points. Your AIDS HQ compounded five times a year for five years. And so the amount is going to be the total that we need. Divided by this factor of one points here. Eight to fifth, minus one over's your point, Your age And the skin is about six eighty one point eight three, six hundred eighty one dollars and eighty three cents her year. We need to deposit. Okay? And now we need to make a table Cashes the deposit schedule. So we have payment number. We have what we actually deposit. So at the end of every year, we'LL have the interest earned and then we'LL have the turtle an account. Get up here. I can't So have five payments within the first year and second year into the third year and its fourth year into this year, Each time we're depositing the same amount. Six. Eighty one eighty three six city one eighty three, sixty one. You three, six maybe one six. Anyone injury. Okay, so after the first year, we just have the amount that we deposited. There wasn't any money, so we didn't have any interest the second year. So we're in interest on the six. Eighty one point eight three. So we had eight percent to that wait earned a percent That which is before twenty five. And then we add that to, um not in the account plus on other deposits and begin toe after the second year. Fourteen, eighteen, twenty one. And then over thirty re earn interest on this melt. So that's, uh, C a percent of fourteen. Eighteen, twenty one. The team put for six. Then we had this into account and another deposit that gives us twenty to one three point. Thank you. True. No, You turn a percent interest on this. Thanks. One seventy seven point zero eight. And then we had another deposit and this interest turned. And we have three thousand seventy two. Forty one sense, OK? And that we have wear an interest on this, which gives over the fifth year to forty five points of nine. Then we have the interest turned in our last payment and we have one thousand dollars in three cents. We compare four thousand dollars and look at that. We had three cents, Doctor

Because the party on this problem, it's fairly simple. The final amount. 60,000. But until then, um, they're paying 8% simple interest quarterly so easy enough, we just take 60,000 of and then times 8%. Okay, it's gonna be 4800. And because it's, uh, quarterly, there isn't divide that by four, and so they're making $1200 month quarterly payments. And that's not so bad for Part B. They're also trying to save up 60,000. So the final value of a sinking fund is 60,000 and they need to know how much to put away to make sure they have enough at the end of the seven years. This is the interest rate on the sinking fund. Annuity is 6% compound. It's semi annually. So we got 0.3 It's compound semi annually, so we multiply by two our number of years, which was seven. And so they didn't even make 14 payments. Okay, so I figured this hours canoe 60,000 eyes equal to our times. 1.3 to the 14th power minus one to about adviser appointed 03 Yes. That's gonna give us 60,000. It was our time service cake A Put that in. So 1.3 for came to power minus one at about 0.3 A multiplier is gonna be 17 when 08 it's, um, change. And if we divide 60,000 by that, we're going to get that the monthly. The quarterly payments are in addition to the 1200 that they're paying for the the interest I'm on that property. They also have to be putting away $3511 come 58 cents into this other child to save up for the 60,000. Okay, thank you very much.

Okay, so you have that Christie puts in. So that's RP 10,500 into account that she wished she wishes to. I'm saved for 12 years, hoping that car would cost 30,000 by then. So that's a is you got to do that and ratifying our great. So that's arm is equal to question Mark given, that's a We have compounded quarterly. Which means that every single to for our equation A is equal to p. Times one plus R over m to the power, uh, 12 times for and then for B, we have compounded continuously. So that's a is equal to P, which is 10,500 times each and five or and T, which is 12. Okay, so let's solve for R both of these cases. So we have also a of 30,000 that I forgot to put it. So let's put that end. So am 30,020 and I would solve for R. So we're gonna divide by 10,500 on both sides. Now we have the following to the power of 12 cents four. That's, um, 48 now on multiply both sides by 1/40 eights to isolate our okay, so I get dirty. Death in divided by $10.500 didn't have won over 48 is equal to one plus R over four, and now all subjects one on both sides and then multiply by four and we get the following. So this minus one and multiply what both sides before. So we get four minus four here is equal to our and I would solve for R to get four times 30,000 divided by 10 500 to the power of 1/48 minus four. Which gives me a rates off 0.88 And that's equal to eight points eight cents for art rates. And what about if the compound continuously so dividing by 10 500 on both sides that you could eat that part on Times 12 and I will take the eligible science to get rid of our base of E. That's even to our times, calls the writing by 12 on both sides, we get on one of 30,000 divided by 10 500 then divided by 12 which gives me rates off 0.87 which is pervades of 8.7%. It's

Whenever we see annuity problems like this one, we should immediately think of the equation. A is equal to p Times one plus I raised to the end power minus one, divided by I. This is given at the end of the most recent chapter of the book, and it's incredibly useful. So here, let's see what we have for each of the variables. First off A. We know that in 10 years we want to have $50,000 in the account, so a is going to equal to $50,000 then p How much are we paying for, period? Well, we don't really know. That's what we're solving for, so we'll leave P blank for now. Then I So I is the interest rate divided by how many times were compounding for years. So the interest rates is 6%. However, 6%. That's equal to 0.6 and then we have to divide by the number of times we're compounding. That is 12 times because we're compounding monthly in their 12 months per year. So I is equal the 120.0 6/12 and finally end and is the number of times this will be compounded. It's the number of periods that we want to have. So we have 10 years times 12 months per year, which will give us 120. So enter the 120 different payment periods. Now that we have all this information we can plug in and solve for Pete. So we have 50,000 is equal to P times. All right, one plus I. That is one plus point No. 6/12. Race to the end power where n is 1 20 minus one, divided by 10.0 6/12. And now that we have this, let's solve and rear entropy. So I plugged this entire term here on the right, into my calculator to get this, we now have 50,000 equals p. Times 1 63.88 and now dividing both sides by 1 63.88 will give us our final answer. P equals $305.10. So if we want to have $50,000 in 10 years, we should put in $305 every month into this account.


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