Final answer:
To find out how long it will take for Reggie and Jennifer's money to double, we can use the formula for compound interest. It will take them approximately 9.90 years, rounded to the nearest month, to double their money.
Step-by-step explanation:
To find out how long it will take for Reggie and Jennifer's money to double, we can use the formula for compound interest: A = P * e^(rt). In this formula, A is the final amount, P is the initial amount (their savings), e is Euler's number (approximately 2.71828), r is the interest rate, and t is the time in years. Since they want their money to double, the final amount will be twice the initial amount. Let's denote their savings as S, so the equation becomes: 2S = S * e^(0.07t).
Simplifying the equation, we get: 2 = e^(0.07t). To solve for t, we need to take the natural logarithm of both sides: ln(2) = 0.07t * ln(e). Since ln(e) is equal to 1, we can simplify further: ln(2) = 0.07t. Now we can solve for t by dividing both sides by 0.07: t = ln(2) / 0.07. Using a calculator, we find that t is approximately 9.90 years. Rounding to the nearest month, it will take Reggie and Jennifer around 9 months to double their money.