Question

Select either method learned to find the term of a savings account to answer the question. Round your answer to one decimal place. Leni opened a savings account that pays 0. 8% interest compounded quarterly. Her initial deposit was $50. How long would she have to leave the money in the account for it to double?.

Answer 1

To find out how long Leni would need to leave the money in the account for it to double, we can use the formula for compound interest. After solving the equation, we find that she would need to leave the money in the account for approximately 7.22 years.

Step-by-step explanation:

To find how long it would take for Leni's money to double in the savings account, we can use the formula for compound interest. The formula is:

A = P(1 + r/n)^(nt)

Where:

• A is the final amount in the account ($100 in this case)
• P is the principal amount (Leni's initial deposit, $50)
• r is the annual interest rate (0.8% or 0.008)
• n is the number of times interest is compounded per year (quarterly)
• t is the time in years

Using this formula, we can solve for t:

100 = 50(1 + 0.008/4)^(4t)

Divide both sides of the equation by 50:

2 = (1.002)^(4t)

Take the natural logarithm of both sides:

ln(2) = ln((1.002)^(4t))

Using the logarithmic property, we can simplify this equation:

ln(2) = 4t * ln(1.002)

Divide both sides of the equation by 4 ln(1.002):

t = ln(2) / (4 * ln(1.002))

Using a calculator, we find that t ≈ 86.6 months or 7.22 years.