Question

How long will it take money to quadruple if it is invested at the following rates? (

A) 3.9% compounded weekly
(B) 7.8% compounded weekly
(A)_____ years
(Round to two decimal places as needed)
(B) ______ years
(Round to two decimal places as needed)

Answer 1

To determine how long it will take for money to quadruple using compound interest at different rates, you can use the formula: Amount = Principal x (1 + Rate/Number of times compounded)^(Number of times compounded x Time). Substituting the given values and solving for Time will give you the answer.

Step-by-step explanation:

To determine how long it will take for money to quadruple using compound interest, we can use the formula:

Amount = Principal x (1 + Rate/Number of times compounded)^(Number of times compounded x Time)

For option A, where the rate is 3.9% compounded weekly, we have:
Amount = Principal x (1 + 0.039/52)^(52 x Time)

For option B, where the rate is 7.8% compounded weekly, we have:
Amount = Principal x (1 + 0.078/52)^(52 x Time)

Solving for Time, we can rearrange the formula:
Time = log(Quadruple Amount/Principal) / (52 x log(1 + Rate/52))

Now we can substitute the values to find the time it takes for the money to quadruple:

For option A:
Time = log(4) / (52 x log(1 + 0.039/52))

For option B:
Time = log(4) / (52 x log(1 + 0.078/52))

Calculating the values will give us the time it takes for the money to quadruple in each case.