At 16% compounded quarterly, how long would it take for money to triple?
To determine how long it would take for money to triple with a 16% interest rate compounded quarterly, we need to use the compound interest formula:
A = P * (1 + r/n)^(n*t)
Where:
A = Final amount of money (triple the original amount)
P = Principal amount (original amount of money)
r = Annual interest rate (16% or 0.16)
n = Number of times the interest is compounded per year (quarterly, so 4 times)
t = Time in years
We want to find the time, t, it takes for P to triple, so we set the final amount, A, to be three times the initial amount:
3P = P * (1 + 0.16/4)^(4*t)
Now, we can simplify the equation:
3 = (1 + 0.04)^(4*t)
Taking the natural logarithm (ln) of both sides of the equation can help us solve for t:
ln(3) = ln((1.04)^(4*t))
Using the logarithmic property, we can bring down the exponent:
ln(3) = 4*t * ln(1.04)
Now, we can isolate t by dividing both sides by 4 * ln(1.04):
t = ln(3) / (4 * ln(1.04))
Using a calculator, we can evaluate this expression to find the value of t.