Question

An investment is made at 2% compounded quarterly, and it grows to $2,000 at the end of 6 years. How much was originally invested?

a) $1,750
b) $1,800
c) $1,850
d) $1,900

Answer 1

To find the original investment for a compound interest account that has grown to $2,000, the formula for compound interest is used, revealing that the initial investment was approximately $1,800.

Step-by-step explanation:

To determine the original investment for an account that grows to $2,000 at a 2% compounded quarterly rate over 6 years, 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 know that A = $2,000, r = 0.02 (2%), n = 4 (quarterly), and t = 6. Plugging these into the formula:

$2,000 = P(1 + 0.02/4)^(4*6)

Now we solve for P:

$2,000 = P(1 + 0.005)^(24)

$2,000 = P(1.005)^24

P = $2,000 / (1.005)^24

P ≈ $1,800

Therefore, the original investment was $1,800, which corresponds to option B.