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Ezzat invests $50 000 in an account which earns 8% interest, compounded annually. He intends to withdraw SM at the end of each year, immediately after the interest has been paid. He wishes to be able to do this for exactly 20 years, so that the account will then be empty. i. How much money does he have in the account immediately after he has made his first withdrawal? Write an expression in terms of M for the amount of money in the account, immediately after his 20th withdrawal. 111. iv. Calculate the value of M which leaves his account empty after the 20th withdrawal. Suppose Ezzat wished to be able to withdraw $8000 per year for the 20 years. By using your calculator alone, estimate, to the nearest per cent, the interest rate he would then need to earn on his account.

Ezzat invests $50 000 in an account which earns 8% interest, compounded annually. He intends to withdraw SM at the end of each year, immediately after the interest has been paid. He wishes to be able to do this for exactly 20 years, so that the account will then be empty. i. How much money does he have in the account immediately after he has made his first withdrawal? Write an expression in terms of M for the amount of money in the account, immediately after his 20th withdrawal. 111. iv. Calculate the value of M which leaves his account empty after the 20th withdrawal. Suppose Ezzat wished to be able to withdraw $8000 per year for the 20 years. By using your calculator alone, estimate, to the nearest per cent, the interest rate he would then need to earn on his account.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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X 09:57 (15)! series&applications_... 13)! Benjamin Franklin left a will in which he established a fund of $1000 for the citizens of Boston. His instructions were that his money was to be invested at 5% interest, compounded annually. i. ¦17)! ii. 14)! A sum of $10 000 is placed in a bank account and earns 12% interest per annum, compounded annually. How much money is in the account at the end of 6 years, just after the final interest has been paid?¤ i. ii. 21)! Page 2 of 16 If Franklin's instructions were followed, how much money would have been in the fund 100 years after it was established? ii. Suppose that at the beginning of each subsequent year after establishment, a further $1000 had been added to the fund and had also earned 5% interest, compounded annually. How much money would have been in the fund after 200 years, just before the next $1000 would have been added to the fund? iii. iv. For what values of r does the geometric series a +ar+ar+ have a limiting sum? For these values of r write down the limiting sum. 1 Find a geometric series with common ratio that has limiting sum 16)! A timber worker is stacking logs. The logs are stacked in layers, where each layer contains one log less than the layer below. There are five logs in the top layer, six logs in the next layer, and so on. There are n layers altogether. i. Write down the number of logs in the bottom layer. ii. Show that there are n (n +9) logs in the stack. tap W first trough 2m-> 3 m 3 m A tap and n water troughs are in a straight line. The tap is first in line, 2 metres from the first trough, and there is 3 metres between consecutive troughs. A stable hand fills the troughs by carrying a bucket of water from the tap to each trough and then returning to the tap. Thus she walks 2 + 2 = 4 metres to fill the first trough, 10 metres to fill the second trough, and so on. i. How far does the stable hand walk to fill the kth trough? How far does the stable hand walk to fill all n troughs? ii. 111. The stable hand walks 1220 metres to fill all the troughs. How many water troughs are there? 19)! The positive multiples of 7 are 7, 14, 21, ... . i. ii. ll 4G second trough 18)! Ezzat invests $50 000 in an account which earns 8% interest, compounded annually. He intends to withdraw $M at the end of each year, immediately after the interest has been paid. He wishes to be able to do this for exactly 20 years, so that the account will then be empty. How much money does he have in the account immediately after he has made his first withdrawal? Write an expression in terms of M for the amount of money in the account, immediately after his 20th withdrawal. 50 cm 1 1-w third trough Calculate the value of M which leaves his account empty after the 20th withdrawal. Suppose Ezzat wished to be able to withdraw $8000 per year for the 20 years. By using your calculator alone, estimate, to the nearest per cent, the interest rate he would then need to earn on his account. What is the largest multiple of 7 less than 1000? What is the sum of the positive multiples of 7 which are less than 1000?¤ Page 3 of 16 ¸¤ 20)! Kim invests $1000 at 8% per year compound interest, compounded quarterly. Calculate the value of the investment after 5 years. 30 cm (22)! Express 0.23 as a fraction. 23)! The third term of an arithmetic series is 32 and the sixth term is 17. i. Find the comme... HUTCHOU. ii Find the sum of the first ten terms A simple instrument has many strings, attached as shown in the diagram. The difference between the lengths of adjacent strings is a constant, so that the lengths of the strings are the terms of an arithmetic series. The shortest string is 30 cm long and the longest string is 50 cm. The sum of the lengths of all the strings is 1240 cm. i. Find the number of strings. ii. Find the difference in length between adjacent strings.
Transcribed Image Text:X 09:57 (15)! series&applications_... 13)! Benjamin Franklin left a will in which he established a fund of $1000 for the citizens of Boston. His instructions were that his money was to be invested at 5% interest, compounded annually. i. ¦17)! ii. 14)! A sum of $10 000 is placed in a bank account and earns 12% interest per annum, compounded annually. How much money is in the account at the end of 6 years, just after the final interest has been paid?¤ i. ii. 21)! Page 2 of 16 If Franklin's instructions were followed, how much money would have been in the fund 100 years after it was established? ii. Suppose that at the beginning of each subsequent year after establishment, a further $1000 had been added to the fund and had also earned 5% interest, compounded annually. How much money would have been in the fund after 200 years, just before the next $1000 would have been added to the fund? iii. iv. For what values of r does the geometric series a +ar+ar+ have a limiting sum? For these values of r write down the limiting sum. 1 Find a geometric series with common ratio that has limiting sum 16)! A timber worker is stacking logs. The logs are stacked in layers, where each layer contains one log less than the layer below. There are five logs in the top layer, six logs in the next layer, and so on. There are n layers altogether. i. Write down the number of logs in the bottom layer. ii. Show that there are n (n +9) logs in the stack. tap W first trough 2m-> 3 m 3 m A tap and n water troughs are in a straight line. The tap is first in line, 2 metres from the first trough, and there is 3 metres between consecutive troughs. A stable hand fills the troughs by carrying a bucket of water from the tap to each trough and then returning to the tap. Thus she walks 2 + 2 = 4 metres to fill the first trough, 10 metres to fill the second trough, and so on. i. How far does the stable hand walk to fill the kth trough? How far does the stable hand walk to fill all n troughs? ii. 111. The stable hand walks 1220 metres to fill all the troughs. How many water troughs are there? 19)! The positive multiples of 7 are 7, 14, 21, ... . i. ii. ll 4G second trough 18)! Ezzat invests $50 000 in an account which earns 8% interest, compounded annually. He intends to withdraw $M at the end of each year, immediately after the interest has been paid. He wishes to be able to do this for exactly 20 years, so that the account will then be empty. How much money does he have in the account immediately after he has made his first withdrawal? Write an expression in terms of M for the amount of money in the account, immediately after his 20th withdrawal. 50 cm 1 1-w third trough Calculate the value of M which leaves his account empty after the 20th withdrawal. Suppose Ezzat wished to be able to withdraw $8000 per year for the 20 years. By using your calculator alone, estimate, to the nearest per cent, the interest rate he would then need to earn on his account. What is the largest multiple of 7 less than 1000? What is the sum of the positive multiples of 7 which are less than 1000?¤ Page 3 of 16 ¸¤ 20)! Kim invests $1000 at 8% per year compound interest, compounded quarterly. Calculate the value of the investment after 5 years. 30 cm (22)! Express 0.23 as a fraction. 23)! The third term of an arithmetic series is 32 and the sixth term is 17. i. Find the comme... HUTCHOU. ii Find the sum of the first ten terms A simple instrument has many strings, attached as shown in the diagram. The difference between the lengths of adjacent strings is a constant, so that the lengths of the strings are the terms of an arithmetic series. The shortest string is 30 cm long and the longest string is 50 cm. The sum of the lengths of all the strings is 1240 cm. i. Find the number of strings. ii. Find the difference in length between adjacent strings.
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