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2. Damian deposits P dollars in a POSD bank at the beginning of a year. The deposit earns an interest rate of x% compounded annually. At the end of each year, of the amount in the account (including principal and interest) is withdrawn and the remainder is re-deposited at the same rate. Let u, denote the amount of money withdrawn at the end of the nth year. (a) Express u, and u₂ in terms of P and x and hence show 3 that u3 = P(1+)³. (b) Given that u₁, U2, U3... forms a geometric progression; find the common ratio in terms of x. 27 -P, find the value of x. Given further 128 that P = 5000, find the total amount of money withdrawn at the end of the first 5 years. Give your answer correct to the nearest integer. (c) Suppose u3 = Answer: (a) u₁ = P(1+2) U₂ = ²/P(1 + x)² (b) r = ²/3 (1 + 100) (c) x= 12.5; 5720

2. Damian deposits P dollars in a POSD bank at the beginning of a year. The deposit earns an interest rate of x% compounded annually. At the end of each year, of the amount in the account (including principal and interest) is withdrawn and the remainder is re-deposited at the same rate. Let u, denote the amount of money withdrawn at the end of the nth year. (a) Express u, and u₂ in terms of P and x and hence show 3 that u3 = P(1+)³. (b) Given that u₁, U2, U3... forms a geometric progression; find the common ratio in terms of x. 27 -P, find the value of x. Given further 128 that P = 5000, find the total amount of money withdrawn at the end of the first 5 years. Give your answer correct to the nearest integer. (c) Suppose u3 = Answer: (a) u₁ = P(1+2) U₂ = ²/P(1 + x)² (b) r = ²/3 (1 + 100) (c) x= 12.5; 5720

Intermediate Algebra
Intermediate Algebra
10th Edition
ISBN:9781285195728
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter11: Exponential And Logarithmic Functions
Section11.2: Applications Of Exponential Functions
Problem 27PS
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2. Damian deposits P dollars in a POSD bank at the beginning of a year. The deposit earns an interest rate of x% compounded annually. At the end of each year, of the amount in the account (including principal and interest) is withdrawn and the remainder is re-deposited at the same rate. Let un denote the amount of money withdrawn at the end of the nth year. (a) Express u, and u₂ in terms of P and x and hence show 3 that u3 = P(1 +³. 27 (b) Given that u₁, U2, U3... forms a geometric progression; find the common ratio in terms of x. (c) Suppose u3 = 27 -P, find the value of x. Given further 128 that P = 5000, find the total amount of money withdrawn at the end of the first 5 years. Give your answer correct to the nearest integer. Answer: (a) u₁ = P(1+) u₂ = ²P (1 + x)² 100 (b) = // (1+500) (c) x = 12.5; 5720
Transcribed Image Text:2. Damian deposits P dollars in a POSD bank at the beginning of a year. The deposit earns an interest rate of x% compounded annually. At the end of each year, of the amount in the account (including principal and interest) is withdrawn and the remainder is re-deposited at the same rate. Let un denote the amount of money withdrawn at the end of the nth year. (a) Express u, and u₂ in terms of P and x and hence show 3 that u3 = P(1 +³. 27 (b) Given that u₁, U2, U3... forms a geometric progression; find the common ratio in terms of x. (c) Suppose u3 = 27 -P, find the value of x. Given further 128 that P = 5000, find the total amount of money withdrawn at the end of the first 5 years. Give your answer correct to the nearest integer. Answer: (a) u₁ = P(1+) u₂ = ²P (1 + x)² 100 (b) = // (1+500) (c) x = 12.5; 5720
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