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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Finding Account Balances In Exercises 19-22, complete the table to determine the balance A for P dollars invested at rate r for t years, compounded n times per year.

n 1 2 4 12 365 Continuous compounding
A

P = $ 7000 ,   r = 6 % ,   t = 20  years

To determine

To calculate: The amount A for corresponding value of n that is, number of times compounded per year in the following table when $7000 is invested at the rate of 6% for 20 years:

n 1 2 4 12 365 Continuous compounding
A
Explanation

Given Information:

The amount of $7000 is invested at the rate of 6% for 20 years and the table is as follows:

n 1 2 4 12 365 Continuous compounding
A

Formula used:

The formula to compute the balance amount after t years when interest is compounded n times per year is,

A=P(1+rn)nt

Where, P is the deposited amount, A is the amount after t years, r is the interest rate in decimals, t is the number of years and n is the number of times compounded per year.

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.

Calculation:

Consider that the amount of $7000 is invested at the rate of 6% for 20 years.

Here, P=$7000, r=6% and t=20 years.

Simplify the rate as,

r=6%=6100=0.06

When n=1,

Substitute 1 for number of times compounded per year, 0.06 for interest rate, $7000 for the amount deposited and 20 years for the time in the formula, “A=P(1+rn)nt” as,

A=P(1+rn)nt=$7000(1+0.061)(1)(20)

Solve further as,

A=$7000(1.06)20$70003.207136$22,449.95

When n=2,

Substitute 2 for number of times compounded per year, 0.06 for interest rate, $7000 for the amount deposited and 20 years for the time in the formula, “A=P(1+rn)nt” as,

A=P(1+rn)nt=$7000(1+0.062)(2)(20)

Solve further as,

A=$7000(1.03)40$70003.262038$22,834.26

When n=4,

Substitute 4 for number of times compounded per year, 0.06 for interest rate, $7000 for the amount deposited and 20 years for the time in the formula, “A=P(1+rn)nt” as,

A=P(1+rn)nt=$7000(1+0

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P-107RECh-4 P-108RECh-4 P-109RECh-4 P-110RECh-4 P-111RECh-4 P-112RECh-4 P-113RECh-4 P-114RECh-4 P-115RECh-4 P-116RECh-4 P-117RECh-4 P-118RECh-4 P-119RECh-4 P-120RECh-4 P-121RECh-4 P-122RECh-4 P-123RECh-4 P-124RECh-4 P-125RECh-4 P-126RECh-4 P-127RECh-4 P-128RECh-4 P-129RECh-4 P-130RECh-4 P-131RECh-4 P-132RECh-4 P-1TYSCh-4 P-2TYSCh-4 P-3TYSCh-4 P-4TYSCh-4 P-5TYSCh-4 P-6TYSCh-4 P-7TYSCh-4 P-8TYSCh-4 P-9TYSCh-4 P-10TYSCh-4 P-11TYSCh-4 P-12TYSCh-4 P-13TYSCh-4 P-14TYSCh-4 P-15TYSCh-4 P-16TYSCh-4 P-17TYSCh-4 P-18TYSCh-4 P-19TYSCh-4 P-20TYSCh-4 P-21TYSCh-4 P-22TYSCh-4 P-23TYSCh-4 P-24TYSCh-4 P-25TYSCh-4 P-26TYSCh-4 P-27TYSCh-4 P-28TYSCh-4 P-29TYS

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