Chapter 4, Problem 23RE

Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

Chapter
Section

Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Comparing Account Balances In Exercises 23 and 24, $2000 is deposited in an account. Decide which account, (a) or (b), will have the greater balance after 10 years.(a) 5%, compounded continuously(b) 6%, compounded quarterly To determine The account which has more balance after 10 years from the following options when an amount of$2000 is invested in an account at the rate of interest which is compounded as:

(a). r=5%, compounded continuously

(b). r=6%, compounded quarterly

Explanation

Given Information:

An amount of $2000 is invested in an account for 10 years at the rate of interest which is compounded as: (a). r=5%, compounded continuously (b). r=6%, compounded quarterly Calculation: Consider that the amount of$2000 is invested in an account for 10 years.

Here, P=$2000 and t=10. Now, consider the part (a) with the interest rate of 5% that is compounded continuously, Simplify the rate as, r=5%=5100=0.05 The formula to compute the balance amount after t years when interest is compounded continuously is, A=Pert Where, P is the deposited amount, A is the amount after t years, r is the interest rate in decimals and t is the number of years. Compute the balance amount by substituting 0.05 for interest rate,$2000 for the amount deposited and 10 years for the time in the formula “A=Pert” as,

A=$2000e(0.05)(10)=$2000e0.5$2000×1.64872=$3297.44

Thus, the balance amount in the account when interest is compounded continuously at the rate of 5% is approximately \$3297.44.

Now, consider the part (b) with the interest rate of 6% that is compounded quarterly,

Simplify the rate as,

r=6%=6100=0

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