Question

Principal: $15,500

Interest rate: 6%

Compounded quarterly

Calculate the effective rate (APY) of interest for 1 year. (Use the Table provided.)

Answer 1

Effective rate (APY) ≈ 6.14 %

Explanation:

The effective rate, also known as the Annual Percentage Yield (APY), takes into account the effect of compounding on the interest earned over a year. The formula for APY is:

`\sf APY = \left(1 + (r)/(n)\right)^n - 1`

where:

-
`\sf r` is the nominal interest rate (in decimal form),

-
`\sf n` is the number of compounding periods per year.

In this case, the nominal interest rate is 6%, so
`\sf r = 0.06`, and the interest is compounded quarterly, so
`\sf n = 4`.

`\sf APY = \left(1 + (0.06)/(4)\right)^4 - 1`

Let's calculate this:

`\sf APY = \left(1 + 0.015\right)^4 - 1`

`\sf APY = (1.015)^4 - 1`

`\sf APY \approx 1.061363550625 - 1`

`\sf APY \approx 0.061363550625`

Now, to express this as a percentage, multiply by 100:

`\sf APY \approx 6.1363550625\%`

`\sf APY \approx 6.14\% \textsf{ (in 2 d.p.) }`

Therefore, the effective annual rate (APY) of interest for 1 year, compounded quarterly, is approximately 6.14%.