Question

If $900 are deposited into an account with

5.5% interest rate, compounded quarterly,
what is the balance after 20 years?
F = $[?]
Round to the nearest cent.

Answer 1

Explanation:

The formula to calculate the future value (F) of an investment with compound interest is:

`\sf{\[ F = P * \left(1 + (r)/(n)\right)^(nt) \]}`

Where:

- ( P ) is the initial principal amount (initial deposit), which is $900 in this case.

- ( r ) is the annual interest rate (as a decimal), which is 5.5% or 0.055.

- ( n ) is the number of times the interest is compounded per year, which is 4 (quarterly).

- ( t ) is the number of years, which is 20.

Plugging in these values:

`\sf{\[ F = 900 * \left(1 + (0.055)/(4)\right)^(4 * 20) \]}`

Calculating this gives approximately $2165.54. Rounded to the nearest cent, the balance after 20 years would be $2165.54.

Answer 2

F = $2683.56

Explanation:

The formula for compound Amount is:

`\sf F = P\left(1 + (r)/(n)\right)^(nt)`

Where:

• F is the future value
• P is the principal amount
• r is the annual interest rate
• n is the number of compounding periods per year
• t is the number of years

In this case, we have:

• P = $900
• r = 5.5% = 0.055
• n = 4 (compounded quarterly)
• t = 20 years

So, the future value is:

`\sf F = 900(1 + (0.055)/(4))^(4* 20)`

`\sf F = 900(1 +0.01375)^(80)`

`\sf F = 900(1.01375)^(80)`

`\sf F = 900* 2.981737296`

`\sf F=2683.563566`

Rounded to the nearest cent, the future value is $2683.56.

Therefore, if $900 are deposited into an account with 5.5% interest rate, compounded quarterly, the balance after 20 years will be $2683.56.