Suppose that money is deposited daily into a savings account at an annual rate of $900. If the account pays 4% interest compounded continuously, estimate the balance in the account at the end of 4 yeam The approximate balance in the account is S (Round to the nearest dollar as needed.)

Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter4: Exponential And Logarithmic Functions
Section4.CT: Chapter Test
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Suppose that money is deposited daily into a savings account at an annual rate of $900. If the account pays 4% interest compounded continuously, estimate the balance in the account at the end of 4 years.
The approximate balance in the account is S
(Round to the nearest dollar as needed.)
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Question Help ▼
Suppose that money is deposited daily into a savings account at an annual rate of $1400. If the account pays
4% interest compounded continuously, estimate the balance in the account at the end of 2 years.
N.
Ke-dt, where money is deposited at a rate of K dollars/year for N years at an interest rate of r.
Use the given information in the definition for the future value.
r(N-1) dt%3D
| 1400 e 0.04(2-)dt
kX + C.
Integrate with respect to t using the rule
1400 e 0.04(2- t)dt = - 35.000 e 0.04(2 -
la-a
0.
Now, evaluate the result over the interval from t 0 to t=2.
- 35,000 e 0.04(2 - 1
= - 35,000 (1- e 08)
N 2915 (rounded to the nearest dollar)
Therefore, the approximate balance in the account after 2 years is $2915.
Transcribed Image Text:Suppose that money is deposited daily into a savings account at an annual rate of $900. If the account pays 4% interest compounded continuously, estimate the balance in the account at the end of 4 years. The approximate balance in the account is S (Round to the nearest dollar as needed.) View an Example Question Help ▼ Suppose that money is deposited daily into a savings account at an annual rate of $1400. If the account pays 4% interest compounded continuously, estimate the balance in the account at the end of 2 years. N. Ke-dt, where money is deposited at a rate of K dollars/year for N years at an interest rate of r. Use the given information in the definition for the future value. r(N-1) dt%3D | 1400 e 0.04(2-)dt kX + C. Integrate with respect to t using the rule 1400 e 0.04(2- t)dt = - 35.000 e 0.04(2 - la-a 0. Now, evaluate the result over the interval from t 0 to t=2. - 35,000 e 0.04(2 - 1 = - 35,000 (1- e 08) N 2915 (rounded to the nearest dollar) Therefore, the approximate balance in the account after 2 years is $2915.
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