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Reggie and Jennifer want to buy the condo they are currently renting. They have some money in a savings account, but the condo costs twice that much. If the account earns 7% interest compounded continuously, how long will it take for their money to double? Round your answer to the nearest month.

a. 8 months
b. 10 months
c. 12 months
d. 15 months

User Pah
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1 Answer

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Final answer:

To find out how long it will take for their money to double, we can use the formula for compound interest: A = P*e^(rt). The initial amount is their savings account balance, which is half the cost of the condo. The final amount is 2P, since they want their money to double. Solving the equation, we find that it will take approximately 10 months for their money to double.

Step-by-step explanation:

To find out how long it will take for their money to double, we can use the formula for compound interest:
A = P*e^(rt),
where A is the final amount, P is the initial amount, r is the interest rate, and t is the time in years.

In this problem, the initial amount is their savings account balance, which is half the cost of the condo. So, P = (1/2)C, where C is the cost of the condo. The final amount is 2P, since they want their money to double. The interest rate is 7% or 0.07, and we need to solve for t.

Putting all the values into the equation, we get 2P = P*e^(0.07t). Dividing both sides by P, we have 2 = e^(0.07t). Taking the natural logarithm of both sides, we get ln(2) = 0.07t. Solving for t, we find t = ln(2)/0.07.

Using a calculator, the value of ln(2)/0.07 is approximately 9.9. Rounding to the nearest month, it will take approximately 10 months for their money to double.

User Ruds
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