Question
Mathematics
At its current growth, a cryptocurrency has a doubling time of 27 dars. Given we today what will the crypto be worth in one year at its current grouth?
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If the cryptocurrency has a doubling time of 27 days, then the daily growth rate can be calculated as:
$r=\frac{1}{{2}^{\frac{1}{27}}}-1$r=(1)/(2^((1)/(27)))-1
Substituting the value:
$r\approx 0.026$r~~0.026
This means that the value of the cryptocurrency is expected to grow by approximately 2.6% per day.
To calculate the value of the cryptocurrency after one year, we need to know how many compounding periods there are in one year. Since there are 365 days in a year and the doubling time is 27 days, we have:
$n=\frac{365}{27}\approx 13.52$n=(365)/(27)~~13.52
This means that there are approximately 13.52 compounding periods in one year.
Now we can use the formula for compound interest to calculate the value of the cryptocurrency after one year:
$A=P\cdot \left(1+r{\right)}^{n}$A=P*(1+r)^(n)
Where:
• A is the final value of the investment.
• P is the initial value of the investment.
• r is the interest rate per compounding period.
• n is the number of compounding periods.
Substituting the given values:
$A=1\cdot \left(1+0.026{\right)}^{13.52}\approx 1.421$A=1*(1+0.026)^(13.52)~~1.421
Therefore, at its current growth rate, the cryptocurrency is expected to be worth approximately 1.421 times its current value after one year.
Step-by-step solution:
1. Calculate the daily growth rate:
• $r=\frac{1}{{2}^{\frac{1}{27}}}-1\approx 0.026$r=(1)/(2^((1)/(27)))-1~~0.026
1. Calculate the number of compounding periods in one year:
• $n=\frac{365}{27}\approx 13.52$n=(365)/(27)~~13.52
1. Substitute the values into the compound interest formula:
• $A=1\cdot \left(1+0.026{\right)}^{13.52}\approx 1.421$A=1*(1+0.026)^(13.52)~~1.421
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