fiona invested $1000 at 6% compounded continuously. at the same time, maria invested $1100 at 6% compounded daily. how long will it take for their investments to be equal in value?
step by step please!
working on adding unlike fractions
2100
To find out how long it will take for Fiona and Maria's investments to be equal in value, we need to set up an equation using the compound interest formula.
The compound interest formula is given by:
A = P * e^(rt)
Where:
A is the amount after time t,
P is the principal amount (initial investment),
e is the base of the natural logarithm (approximately 2.71828),
r is the annual interest rate, and
t is the time in years.
Let's calculate the amount of Fiona's investment after time t:
A_fiona = P_fiona * e^(rt_fiona)
Where:
P_fiona = $1000 (Fiona's initial investment),
r = 6% = 0.06,
t_fiona = the time in years for Fiona's investment.
Similarly, let's calculate the amount of Maria's investment after time t:
A_maria = P_maria * (1 + r_maria/n_maria)^(n_maria*t_maria)
Where:
P_maria = $1100 (Maria's initial investment),
r_maria = 6% = 0.06,
n_maria = number of times the interest is compounded per year (in this case, daily compounding),
t_maria = the time in years for Maria's investment.
Since we want to find the time it takes for their investments to be equal, we can set the two equations equal to each other:
P_fiona * e^(rt_fiona) = P_maria * (1 + r_maria/n_maria)^(n_maria*t_maria)
Substituting the given values:
$1000 * e^(0.06t_fiona) = $1100 * (1 + 0.06/365)^(365*t_maria)
Now we can solve this equation to find the time it takes for their investments to be equal. Since it involves exponential functions, it's easier to solve for the variable using numerical methods or by using a calculator or spreadsheet software.