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Question 2 (25 marks)Find the effective rate for 1* = 8% compounded monthly.marks)b) James borrowed $3,500 from a bank for his business setup. He plans to repay the...

Question

Question 2 (25 marks)Find the effective rate for 1* = 8% compounded monthly.marks)b) James borrowed $3,500 from a bank for his business setup. He plans to repay the debt in a single payment after 4 years. If the interest rate is 7% compounded quarterly, how much is the single payment? marks)Continued. _RAR1/6BMTLAMANAGERIALMATHEMATICS2020What is the future value ofan ordinary annuity at the end of 5 years if $370 is deposited each month into an account earning 2.4% compounded monthly? marks)If S

Question 2 (25 marks) Find the effective rate for 1* = 8% compounded monthly. marks) b) James borrowed $3,500 from a bank for his business setup. He plans to repay the debt in a single payment after 4 years. If the interest rate is 7% compounded quarterly, how much is the single payment? marks) Continued. _ RAR 1/6 BMTLA MANAGERIALMATHEMATICS 2020 What is the future value ofan ordinary annuity at the end of 5 years if $370 is deposited each month into an account earning 2.4% compounded monthly? marks) If S300,000 is to be saved over 25 years, how much should be deposited quarterly if the investment earns 8% interest compounded quarterly? marks) Ryan bought a car with a down payment of RM 3,200 and payments of RM 650 per month for 10 years. If the interest rate is 3% compounded monthly, compute the purchase price of the car and the total interest paid. marks)



Answers

Find the future value of each ordinary annuity, if payments are made and interest is compounded as given. Then determine how much of this value is from contributions and how much is from interest.
$R=1250 ; 5 \%$ interest compounded semiannually for 18 years

Potentially the future value of an ordinary annuity with periodic contributions of $12,000 into an interest rate account of 4.8 percent for 16 years, Get a piece of information given is that the interest is compounded quarterly. Um, so if its quarterly, that means that's happened four times per year. So our end value and 7 16 is gonna be compounded 64 times in the interest rate and said being 4.8% I'm gonna divide that. But for cause being compounded four times a year, just be 1.2% or 0.12 I guess our formula for the future value, uh, is our values. 12,000 times are one plus our interest rates of 1.12 to the 64th power minus one old about of our interest rate of 0.12 Yes, that's gonna be 12,000 times. I'm gonna do that desk on the calculator. So 1.12 to the 64th power I divided by 0.12 the 95.46 and some change. We want to keep that change because we're going to multiply about 12,000. So keep that never in your calculator. Multiple. About 12,000. Give us over a $1,000,000. So one million, 145,000 6 19 Ah, and 96 cents rounded to the nearest set. OK, so that's our total amount. Because problem also wanted to know how much we have from contributions. So that's just gonna be 12,000. And we contributed 64 times. So 12,000 times 64 $768,000. So it's settled from contributions, is there? And so our interest would just be the difference between our contributions and our total eso. I'm just going to subtract this to number. So back to the calculator to the total from interest was $377,000 um, 619 and 96 cents. There's our interest. There's our total contributions. And there's our total value. The ordinary annuity. Thank you very much.

This question we are given with amount investor that speakeasy for two dollars 15,000 time is equal to 80 years. They helping Prestes 5% that 0.5 and we need to find amount earned for various compounding periods by using The formula is equal to be one plus r by N raise to depart. And so in a part, we have compounded and really so compounded animal remains. The compounding period is just once a year, so n value is one so amount is equal to dollars 15,000 multiplied by one plus 0.5 divided by Ivan raised to the power one multiplied by eight. So if we simplify this, we get dollar to 161.83 in V part. We have compounded quarterly compounded quarterly means the compounding period is four times a year. So the very off and this for so we get is equal to $1.15,000 one plus 0.5 divided by four one four multiplied by eight. So if we saw this, we get dollar 2 to 3 to 1.96 Now see part is compounded Monte compounding mentally means the compound big period is each month they're pissed and he's equal with. So if any is equal toe well, the A mountain will be all of 15,000 Marty plied by one plus 0.5 divided fight Well, this to depart well multiplied by eight. So if we simplify this, we get answers. S the 12358.78 For deep part, we need to find the company amount for compounding. Baby That IHS and will you is 3 65 for any is equal to 3 65 we get among is equal do dollar 15,000 multiplied by one plus 0.5 divided by 3 65 The whole race to depart 3 65 multiplied by a again If this all this we get don't do 376.76 then for e part we have compounded contingency So compounded continuously means the formula changes on the formula Toby used This is equal toe be it is to depart rt so if it plug in the values we have $15,000. 15,000 multiplied by it is to depart 0.5 multiplied by eight. So if this all this, we get Darla do 2377.37 Next. We need to compare the amount values as they compounded. Pdf changes so we can see that as compounded period increases, the amount slightly increases.

Calculate the future value of a ordinary annuity. So the payments being put in our $800 the interest being calculated is 6.51 percent and the number of years there's 12. Now the add a piece of information here is that, uh, it's calm, pounded semi annually, so semi annually means, uh, it's happening twice per year. So are in for a formula will be double since it's happening twice per year and our interests will be half because it's happening twice per year. So our interest is gonna be 0.0, uh, three, 755 We just double check that. No stooping to 55 to Okay, So our formula for now, but we have everything set is our 800 times one plus our interest rates of 1.3 to 5 to the eighth Power, which is 24 tu minus one and then divided by our interest rate says 0.3 55 Okay, so it's just gonna equal 800 times. And I was gonna put all that in our calculator. So you at 1.3 to 55 to the 24th power minus one, but about 0.3 to 55 Is that total amount? Our multiplier is gonna be 35.5. Foreign. Some change came out to bind. About 800 gives us our total future annuity. It's 28,438 on and 21 sets. Yes, that's our total. Okay, so from our contributions, it's called C. We just need 800 we made 24 deposits, So 800 times 24. 19,200 star amount from contributions was 19 19,200. Which means if we subtract that from our total, we will get how much interest paid out. The interest paid out. 9238 and I got that bus just attracting our contributions from our total case in interest paid 9238 and 21 cents. Our contributions was 19,200 for a total annuity of 28,400 bus. Okay, thank you very much.

So what is the value off 8000 investment after five years? If it ends, 8% annual interest compounded quarterly. So to solve their suggesting that we use the compound interest formula is usually a is equals toe p one plus I to the park n where P is. The original value on our P in this case is 8000. And, uh, I is the interest rate, and the interest rate in this case is 8% compounded quarterly. So how many quarters for? So we divided by four. And, um, we also need end, which is the number of quarters that are in the the five year period. So it's five years in each year you've got four quarters. So in total, we have got 20 quarters. Well, this is what we we just lead. So the first part, what is the interest rate? Ricotta is 8% divided by four, which is 2% which is equal to 2%. And for our A is equal, A is 8% divided by four, which is 2%. And our pieces how many compound periods? Quarters are five years. So in five years there are four quarters p a making it 20 quarters in the sea, it says find the value of the investment after five years. So a is equal student always obstructing our p is 8000 and one class to present and all to the power. 20 8001.72 on points. There are two to the power 20 which give us 11,887 0.58 told us, but was it?


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