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Math
CalculusCalculus: Early Transcendentals8th Edition

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Chapter 3.8, Problem 20E
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Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550

Solutions

Chapter
Section
Problem 1E
Problem 2E
Problem 3E
Problem 4E
Problem 5E
Problem 6E
Problem 7E
Problem 8E
Problem 9E
Problem 10E
Problem 11E
Problem 12E
Problem 13E
Problem 14E
Problem 15E
Problem 16E
Problem 17E
Problem 18E
Problem 19E
Problem 20E
Problem 21E
Problem 22E
BuyFindarrow_forward

Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550
Textbook Problem

(a) If $1000 is borrowed at 8% interest, find the amounts due at the end of 3 years if the interest is compounded (i) annually, (ii) quarterly. (iii) monthly, (iv) weekly, (v) daily, (vi) hourly, and (vii) continuously.

(b) Suppose $ 1000 is borrowed and the interest is compounded continuously. If A(t) is the amount due after t years, where 0 ≤ t ≤ 3, graph A(1) for each of the interest rates 6%, 8%, and I 0% on a common screen.

(a)

To determine

To find: The amounts due to the end of 3 years if the interest compounded (i) annually, (ii) quarterly, (iii) monthly, (iv) weekly, (v) daily, (vi) hourly, and (vii) continuously.

Explanation

Given:

Initial amount is $1000.

Interest rate is 8%.

Number of years is 3.

Formula used:

The value of the investment is A(t)=A0(1+rn)nt.

Where,

A0 is the initial investment.

r is the interest rate.

n is the number of times the interest is compounded per year.

t is the number of years.

Calculation:

Section (i)

If n=1, the amount of A(3) is computed as follows,

Substitute A0=1000,r=0.08 and t=3 in A(t)=A0(1+rn)nt

A(3)=(1000)(1+0.081)1(3)=(1000)(1+0.08)3=(1000)(1.08)3=1259.71

Thus, the amount is A(3)=1259.71.

Section (ii)

If n=4, the amount of A(3) is computed as follows,

Substitute A0=1000,r=0.08 and t=3 in A(t)=A0(1+rn)nt

A(3)=(1000)(1+0.084)4(3)=(1000)(1+0.02)12=(1000)(1.02)12=1268.24

Thus, the amount is A(3)=1268.24.

Section (iii)

If n=12, the amount of A(3) is computed as follows,

Substitute A0=1000,r=0.08 and t=3 in A(t)=A0(1+rn)nt

A(3)=(1000)(1+0.0812)12(3)=(1000)(1+0.0066666)36=(1000)(1.0066666)36=1270.24

Thus, the amount is A(3)=1270.24.

Section (iv)

If n=52, the amount of A(3) is computed as follows,

Substitute A0=1000,r=0.08 and t=3 in A(t)=A0(1+rn)nt

A(3)=(1000)(1+0

(b)

To determine

To sketch: The graph of amount A(t) due after t years for each of the interest rates 6%,8% and 10%.

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