Question

Say you have invested $45000 at a yearly interest rate of 16% compounded weekly. How many years will it take for your investment to double in size? Years =

Answer 1

Using the compound interest formula, it takes approximately 4.4 years for a $45,000 investment at a yearly interest rate of 16% compounded weekly to double in size.

Step-by-step explanation:

To determine how many years it will take for an investment to double in size at a given interest rate compounded weekly, we use the formula for compound interest: A = P(1 + r/n)^(nt), where:

• A is the amount of money accumulated after n years, including interest.
• P is the principal amount (the initial amount of money).
• r is the annual interest rate (decimal).
• n is the number of times that interest is compounded per year.
• t is the time the money is invested for, in years.

We're looking to find t when the investment doubles, so A = 2P. Plugging in the values, we have:

2 * $45,000 = $45,000(1 + 0.16/52)^(52t)

To solve for t, we divide both sides by $45,000, and then take the natural log of both sides:

2 = (1 + 0.16/52)^(52t)

ln(2) = 52t * ln(1 + 0.16/52)

t = ln(2) / (52 * ln(1 + 0.16/52))

Using a calculator, we find that t ≈ 4.4 years.