(a) Explanation Given: The accumulate amount in 8 years is $ 20000 at 6 % interest rate compounded quarterly. Concept: “The expression for Amount of Annuity is given below. The amount S of an annuity of payments of R dollars each, made at the end of each period for n consecutive interest periods at a rate of interest i per period is given by S = R [ ( 1 + i ) n − 1 i ] .” Calculation: It is given that the value of S is $ 20000 . Now, the value of i if the payments are made at the end of each quarter is i = 6 % 4 . It is simplified as follows: i = 6 400 = 0.015 Therefore, the interest compounded quarterly is i = 0.015 . The number of periods quarterly for 8 years is given below. n = 4 ⋅ 8 = 32 periods Substitute 20000 for S , 0 (b) To determine The payment at the end of each quarter to accumulate $ 20000 in 8 years at 4 % interest rate compounded quarterly.

Calculus with Applications Books a la Carte Edition

11th Edition

ISBN: 9780133864564

Author: Margaret L. Lial; Nathan P. Ritchey; Raymond N. Greenwell

Publisher: Pearson Education

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Chapter 12.2, Problem 33E

(a)

To determine

The payment at the end of each quarter to accumulate $20000 in 8 years at 6% interest rate compounded quarterly.

(b)

To determine

The payment at the end of each quarter to accumulate $20000 in 8 years at 4% interest rate compounded quarterly.

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Chapter 12.2, Problem 32E

Chapter 12.2, Problem 34E

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Calculus with Applications Books a la Carte Edition

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The payment at the end of each quarter to accumulate $ 20000 in 8 years at 6 % interest rate compounded quarterly.