Answer: A = P(1 + r/n)^(nt)
= $630(1 + 0.04375/12)^(12*14.891)
≈ $1528.25
Step-by-step explanation: We can start by using the formula for compound interest, which is given by:A = P(1 + r/n)^(nt)
For Mackenzie, we have:P = $630
r = 4.375% = 0.04375 (4 3/8% as a decimal)
n = 12 (compounded monthly)
t = the time it takes for Amira's money to triple in valueFor Amira, we have:P = $630
r = 4.25% = 0.0425 (4 1/4% as a decimal)
n = continuous compounding
t = ln(3)/(r)
where ln denotes the natural logarithm.
To find the time it takes for Amira's money to triple in value, we can use the formula for continuous compounding, which is given by: A = Pe^(rt)where e is the mathematical constant approximately equal to 2.71828. We want to solve for t when A = 3P, so we have: 3P = Pe^(rt)Dividing both sides by P, we get: 3 = e^(rt)Taking the natural logarithm of both sides, we get: ln(3) = rtSolving for t, we get: t = ln(3)/rSubstituting the given values, we get:t = ln(3)/0.0425 ≈ 14.891 years
So, after about 14.891 years, Amira's money will have tripled in value. Now, we can use the formula for compound interest to find how much money
Mackenzie would have in her account after the same amount of time. We have:
A = P(1 + r/n)^(nt)
= $630(1 + 0.04375/12)^(12*14.891)
≈ $1528.25