Using continuous compounding, it is found that:
a) The account will be worth $26,916.31 in 10 years.
b) It will take 42.18 years for the account to be worth $70,000.
What is compound interest?
The amount of money earned, in continuous compounding, after t years, is given by:
[tex]A(t) = Pe^{rt}[/tex]
In which:
- A(t) is the amount of money after t years.
- P is the principal(the initial sum of money).
- r is the interest rate(as a decimal value).
The parameters are given as follows:
A(0) = 20000, r = 0.0297, t = 10.
Hence the worth in 10 years will be given by:
[tex]A(t) = Pe^{rt}[/tex]
[tex]A(10) = 20000e^{0.0297 \times 10}[/tex]
A(10) = $26,916.31.
Now, we find in how many years it will be worth $70,000, as follows:
[tex]A(t) = Pe^{rt}[/tex]
[tex]70000 = 20000e^{0.0297t}[/tex]
[tex]e^{0.0297t} = 3.5[/tex]
[tex]\ln{e^{0.0297t}} = \ln{3.5}[/tex]
[tex]0.0297t = \ln{3.5}[/tex]
[tex]t = \frac{\ln{3.5}}{0.0297}[/tex]
t = 42.18 years.
More can be learned about continuous compounding at https://brainly.com/question/24722580
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