Question

If ​$3,000 is invested at 3​% compounded quarterly, what is the
amount after 5 ​years?

Answer 1

$3,488.64

Explanation:

To calculate the amount after 5 years with an initial investment of $3,000 at a 3% interest rate compounded quarterly, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = the final amount

P = the principal (initial investment)

r = the annual interest rate (in decimal form)

n = the number of times the interest is compounded per year

t = the number of years

In this case, P = $3,000, r = 3% or 0.03 (since it's given in percentage), n = 4 (quarterly compounding), and t = 5 years.

Substituting the values into the formula:

A = 3000(1 + 0.03/4)^(4*5)

Simplifying the expression within the parentheses:

A = 3000(1 + 0.0075)^(20)

Calculating the value within the parentheses:

A = 3000(1.0075)^(20)

Using a calculator or performing the calculations:

A ≈ 3000 * 1.162881

A ≈ $3,488.64

Therefore, the amount after 5 years would be approximately $3,488.64.

Answer 2

Answer: $3,483.55

Explanation:
Interest Formula: A = P(1 + r/n)^nt

First, convert R as a percent to r as a decimal

r = R/100

r = 3/100

r = 0.03 rate per year,

Then solve the equation for A

A = P(1 + r/n)nt

A = 3,000.00(1 + 0.03/4)(4)(5)

A = 3,000.00(1 + 0.0075)(20)

A = $3,483.55

Summary:

The total amount accrued, principal plus interest, with compound interest on a principal of $3,000.00 at a rate of 3% per year compounded 4 times per year over 5 years is $3,483.55.