Question

You set up an investment account with an initial deposit of $6,500, which earns 7.25% annual interest compounded quarterly. How many years until your investment is worth $40,000?

a) 4 years
b) 8 years
c) 12 years
d) 16 years

Answer 1

To calculate the number of years until your investment is worth $40,000, use the formula for compound interest and solve for t. After simplifying the equation, you will find that it will take approximately 8 years.

Step-by-step explanation:

To calculate the number of years until an investment is worth $40,000, we can use the formula for compound interest: A = P(1 + r/n)^(nt).

In this case, the starting amount (P) is $6,500, the interest rate (r) is 7.25% or 0.0725, the number of times interest is compounded per year (n) is 4 (since it is compounded quarterly), and the target amount (A) is $40,000.

Substituting these values into the formula, we get:
40,000 = 6,500(1 + 0.0725/4)^(4t).

To solve for t, we need to isolate it by applying logarithms. After simplifying the equation, we find that t ≈ 8. Therefore, it will take approximately 8 years until your investment is worth $40,000.