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Sagot :
Answer:
It will take 30.48 for the money in his account to double.
Step-by-step explanation:
Interest compounded anually:
With an investment of P, the amount compounded annualy after t years that you will have is given by:
[tex]A(t) = P(1+r)^{t}[/tex]
In which r is the interest rate, as a decimal.
Ren sets aside $1,000 into an online savings account with an annual interest rate of 2.3%
This means that [tex]P = 1000, r = 0.023[/tex]. So
[tex]A(t) = P(1+r)^{t}[/tex]
[tex]A(t) = 1000(1+0.023)^{t}[/tex]
[tex]A(t) = 1000(1.023)^{t}[/tex]
How long will it take for the money in his account to double?
This is t for which A(t) = 1000*2 = 2000. So
[tex]A(t) = 1000(1.023)^{t}[/tex]
[tex]2000 = 1000(1.023)^{t}[/tex]
[tex](1.023)^{t} = \frac{2000}{1000}[/tex]
[tex](1.023)^{t} = 2[/tex]
[tex]\log{(1.023)^{t}} = \log{2}[/tex]
[tex]t\log{1.023} = \log{2}[/tex]
[tex]t = \frac{\log{2}}{\log{1.023}}[/tex]
[tex]t = 30.48[/tex]
It will take 30.48 for the money in his account to double.
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