Question

If you invest $500 at 1.5% compounded quarterly, how many years does it take for your investment to grow to $1,250? Use the following formula to determine your solution: A = P(1 + r/n)^(nt)

a) 1276.67 years
b) 80.13 years
c) 319.17 years
d) 79.79 years

Answer 1

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.