A principal earns 7% per year simple interest. How long will it take for the future value to quadruple?
consider $1
to obtain 4 times the $1, we need $3 in interest
3 = 1(.07)(t)
t = 3/.07 = appr 42.9 years
check:
consider $100
interest at 7% for 42.9 years
= 100(.07)(42.9 = 300.3
so add that to the 100 we started with, we get 400.3
To find out how long it will take for the future value to quadruple, we can use the formula for simple interest:
FV = PV(1 + rt)
Where:
FV = Future Value
PV = Principal Value
r = interest rate
t = time in years
We know that the principal earns 7% per year, so the interest rate (r) is 7% expressed as a decimal, which is 0.07. We want to find out how long it will take for the future value (FV) to quadruple, so the future value will be 4 times the principal value (PV):
FV = 4 * PV
Substituting the values into the formula, we have:
4 * PV = PV(1 + 0.07t)
Simplifying the equation, we get:
4 = 1 + 0.07t
Subtracting 1 from both sides of the equation, we have:
3 = 0.07t
Dividing both sides of the equation by 0.07, we find:
t = 3 / 0.07
Calculating the result, we have:
t ≈ 42.86 years
Therefore, it will take approximately 42.86 years for the future value to quadruple.
To calculate the time needed for the future value to quadruple, we need to use the formula for simple interest:
Future Value = Principal + (Principal * Interest Rate * Time)
In this case, our goal is to find the time it takes for the future value to quadruple. Let's assume the initial principal is P, and the future value after time T is 4P.
Using the formula, we get:
4P = P + (P * 0.07 * T)
Simplifying the equation, we have:
4P = P + 0.07PT
Rearranging the equation, we get:
4P - P = 0.07PT
3P = 0.07PT
Dividing both sides by PT, we have:
3/P = 0.07T
To isolate the variable T, we multiply both sides by P/0.07:
T = (3/P) / 0.07
Using this formula, we can find the time it takes for the future value to quadruple by dividing 3 divided by the principal (P), and then dividing that result by 0.07.