Question

A principal amount of $1,100 is placed in a savings account with an annual interest rate of 5.95% compounded quarterly. How much interest does the account earn after 12 years? a. $2,246.36 b. $2,234.58 c. $1,146.36 d. $1,134.58

Answer 1

The closest option is d: $1,134.58.

To calculate the interest earned on a savings account compounded quarterly, you can use the formula for compound interest:

`\[ A = P \left(1 + (r)/(n)\right)^(nt) \]`

where:

A is the future value of the investment/loan, including interest.

P is the principal amount (the initial deposit or loan amount).

r is the annual interest rate (decimal).

n is the number of times that interest is compounded per year.

t is the number of years.

In this case:

P = $1,100

r = 0.0595 (5.95% expressed as a decimal)

n = 4 (compounded quarterly)

t = 12 years

Let's substitute these values into the formula:

`\[ A = 1100 \left(1 + (0.0595)/(4)\right)^(4 * 12) \]`

`\[ A \approx 1100 * (1.014875)^(48) \]`

`\[ A \approx 1100 * 2.24636 \]`

`\[ A \approx 2,470 \]`

Now, to find the interest earned, subtract the principal $1,100 from the future value $2,470:

`\[ \text{Interest} = \$2,470 - \$1,100 \]`

`\[ \text{Interest} = \$1,370 \]`

Therefore, the interest earned after 12 years is approximately $1,370.