(21 marks) Course Journal or e-Journal. 60. A 500 investment...

(21 marks) Course Journal or e-Journal. 60. A $500 investment earns 9% compounded semi-annually for 10 years. Without using the TVM Solver, calculate the final value of the investment. Show your work. (3 marks) 61. Without using the TVM Solver, calculate how much money would have to be invested today for the investment to be worth $100 000 in 9 years. The investment earns 8% compounded quarterly. Show your work. (3 marks) 62. Suppose you are given $800 to invest. In one sentence, state which type of interest—10% simple interest or 9.5% interest compounded monthly—offers the best investment for a 5-year term. Give a reason for your answer and provide accurate calculations to support your reasoning. (6 marks)

Transcript

00:02 Hello, the compound interest formula is the amount after t years is equal to p times 1 plus r.

00:12 R is the rate in fractions or decimals over n where n is the periods at which the interest is compounded.

00:24 How many periods are there in one year? it is a number of periods in one year at which the interest is compounded to the power nt where t is the time in years.

00:39 In the first question we are given that the principal is 8000, t is 6, r is 5 percent and it is compounded annually so there is a only one period in one year so n equal to 1.

00:53 We have to find a.

00:56 A is equal to 8000 into 1 plus 5 percent r is equal to 0 .05, n equal to 1 so we just leave it n equal to 1 and t is equal to 6 and we when we calculate this we get this to be equal to 10 ,720 dollars 0 .77 cents approximately equal to.

01:34 In the second question we are given that at maturity the amount is 10 ,000 dollars, the rate of interest per annum was 3 percent, t was 7 years and it was interest was compounded monthly so there are 12 periods in one year.

01:54 We are asked to find what was the initial investment or what was the principal.

02:00 So the principal is equal to the amount divided by principal equal to amount divided by this whole thing which is 1 plus r by n to the power nt which would be in this case 10 ,000 divided by 1 plus r is 3 percent which is 0 .03 and n is 12 this is 0 .03 divided by 12 to the power 12 times 7 12 times 7 and this once you calculate this it comes out to be 8107, 8107 dollars and 97 cents approximately.

03:13 Since these are there are a lot of decimals where we can only give it approximations up to the nearest cent this is 97 cent...

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