Solution Found!
uously, the amount of money increases at a rate
Chapter 3, Problem 10E(choose chapter or problem)
When interest is compounded continuously, the amount of money increases at a rate proportional to the amount S present at time t, that is, dS/dt = rS, where r is the annual rate of interest.
(a) Find the amount of money accrued at the end of 5 years when $5000 is deposited in a savings account drawing \(5 \frac{3}{4} \%\) annual interest compounded continuously.
(b) In how many years will the initial sum deposited have doubled?
(c) Use a calculator to compare the amount obtained in part (a) with the amount \(S=5000\left(1+\frac{1}{4}(0.0575)\right)^{5(4)}\) that is accrued when interest is compounded quarterly.
Text Transcription:
5 3/4 %
S = 5000 (1+1/4(0.0575))^5(4)
Questions & Answers
QUESTION:
When interest is compounded continuously, the amount of money increases at a rate proportional to the amount S present at time t, that is, dS/dt = rS, where r is the annual rate of interest.
(a) Find the amount of money accrued at the end of 5 years when $5000 is deposited in a savings account drawing \(5 \frac{3}{4} \%\) annual interest compounded continuously.
(b) In how many years will the initial sum deposited have doubled?
(c) Use a calculator to compare the amount obtained in part (a) with the amount \(S=5000\left(1+\frac{1}{4}(0.0575)\right)^{5(4)}\) that is accrued when interest is compounded quarterly.
Text Transcription:
5 3/4 %
S = 5000 (1+1/4(0.0575))^5(4)
ANSWER:Step 1 of 6
a) In this problem we need to find the amount of money accrued at the end of 5 years when $5000 is deposited in a savings account drawing annual interest compounded continuously.