Compound Interest Calculation: How Long Will It Take for Your Investment to Double?
What is the formula for compound interest, and how long will it take for an investment of $2,500 to grow to $5,000 at an annual interest rate of 4.55%?
Final answer: It will take approximately 15.2 years for an investment of $2,500 to grow to $5,000 at an annual interest rate of 4.55%, using the formula for compound interest.
Understanding Compound Interest and Growth
Compound interest is the interest calculated on the initial principal and also on the accumulated interest from previous periods. This means that the interest earned each period is added to the principal, and the interest for the next period is then calculated on the new total.
Using the Compound Interest Formula
The formula for compound interest is:
A = P(1 + r)n
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 years the money is invested or borrowed for.
Solving for the Investment Growth
To determine how long it will take for an investment of $2,500 to grow to $5,000 at a rate of 4.55% annually, we can plug in the values into the compound interest formula:
$5,000 = $2,500(1 + 0.0455)n
Calculating the Time Period
To find the number of years (n), we can use logarithms to solve for it:
n = ln(2) / ln(1.0455)
Calculating this gives us approximately 15.2 years for the investment to reach $5,000.
Therefore, the correct answer is (b) 15.2 years.