Final answer:
To determine how many years it takes for $500 to grow to $1,250 at 1.5% interest compounded quarterly, we use the compound interest formula. By solving the formula for time, it takes approximately 79.79 years for the investment to reach the target amount.
Step-by-step explanation:
To calculate how many years it takes for an investment of $500 at 1.5% interest compounded quarterly to grow to $1,250, we can use the compound interest formula 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 in years.
In this case:
- A = $1,250
- P = $500
- r = 0.015 (1.5% expressed as a decimal)
- n = 4 (compounded quarterly)
We need to solve for t. The equation becomes:
1,250 = 500(1 + 0.015/4)^(4t)
To solve for t, we'll need to use logarithms. After rearranging the equation and solving, t is found to be approximately 79.79 years. Therefore, the correct answer is (d) 79.79 years.