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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

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BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
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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Explain the role of voluntary participation in informed consent.

Research Methods for the Behavioral Sciences (MindTap Course List)

Explain how increasing the size of the sample can influence the outcome of a hypothesis test.

Research Methods for the Behavioral Sciences (MindTap Course List)

Compute 4.8911.34 .

Mathematics For Machine Technology