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aryal191
18.02.2021 •
Mathematics
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Ответ:
Part 1) 8.17 years
Part 2) 4.98 years
Part 3) 4.95 years
Part 4) 4.95 years
Step-by-step explanation:
we know that
The compound interest formula is equal to
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
Part 1) Determine the time necessary for P dollars to double when it is invested at interest rate r=14% compounded annually
in this problem we have
substitute in the formula above
Apply log both sides
Part 2) Determine the time necessary for P dollars to double when it is invested at interest rate r=14% compounded monthly
in this problem we have
substitute in the formula above
Apply log both sides
Part 3) Determine the time necessary for P dollars to double when it is invested at interest rate r=14% compounded daily
in this problem we have
substitute in the formula above
Apply log both sides
Part 4) Determine the time necessary for P dollars to double when it is invested at interest rate r=14% continuously
we know that
The formula to calculate continuously compounded interest is equal to
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
e is the mathematical constant number
we have
substitute in the formula above
Simplify
Apply ln both sides
Remember that ln(e)=1