Question

Find the accumulated amount A if the principal P is invested at the interest rate of r/year for t years. (Round your answer to the nearest cent.) P= $46,000, r = 5.1%, t = 11, compounded quarterly

A= ________

Answer 1

To find the accumulated amount of a $46,000 investment at a 5.1% annual interest rate compounded quarterly for 11 years, we use the compound interest formula A = P(1 + r/n)^(nt). The accumulated amount is approximately $79,036.74.

Step-by-step explanation:

We are asked to find the accumulated amount A when $46,000 is invested at an interest rate of 5.1% per year, for 11 years, compounded quarterly. To solve this, we use the formula for compound interest: A = P(1 + r/n)^(nt), where P is the principal amount, r is the annual interest rate (as a decimal), n is the number of times interest is compounded per year, and t is the time the money is invested for in years.

Here, P = $46,000, r = 5.1% or 0.051, n = 4 (since interest is compounded quarterly), and t = 11 years.

The formula becomes: A = $46,000(1 + 0.051/4)^(4×11)

Calculating this:

• A = $46,000(1 + 0.01275)^(44)
• A = $46,000(1.01275)^(44)
• A = $46,000 × (1.71819)
• A = $79,036.74

Hence, the accumulated amount A after 11 years, compounded quarterly, would be approximately $79,036.74, rounded to the nearest cent.