Question

Suppose that $2000 is invested at a rate of 2.8%, compounded quarterly. Assuming that no withdrawals are made, find the total amount after 5 years.

Answer 1

The total amount after 5 years with a $2000 investment at 2.8% interest rate, compounded quarterly, will be approximately $2297.71.

Step-by-step explanation:

To find the total amount after 5 years when $2000 is invested at a rate of 2.8%, compounded quarterly, we can use the compound interest formula:

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

Where:

• Plugging our values into the formula, we get:

A = 2000 (1 + (0.028/4))^(4'5) = 2000 (1 + 0.007))20 = 2000 ( 1.007)^20

Now calculate the exponent and multiply by the principal:

A = 2000 (1.14885

A = $2297.71 (rounded to two decimal places)

The total amount after 5 years will be approximately $2297.71.

To find the total amount after 5 years, we can use the formula for compound interest:

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

where A is the total amount, P is the principal amount (initial investment), r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.

For this problem, the principal amount is $2000, the annual interest rate is 2.8% (or 0.028), interest is compounded quarterly (n = 4), and we want to find the total amount after 5 years (t = 5).

Plugging in these values into the formula, we get:

A = 2000(1 + 0.028/4)^(4*5) ≈ $2297.25

Answer 2

To calculate the total amount of the investment after 5 years with compound interest, the formula A = P(1 + r/n)^(nt) is used. Applying this to an initial investment of $2000 at a 2.8% annual rate, compounded quarterly, results in approximately $2297.05.

Step-by-step explanation:

To calculate the total amount of an investment over a certain period with compound interest, we use the formula A = P(1 + r/n)^(nt), where:

• A = the future value of the investment/loan, including interest
• P = the principal investment amount ($2000 in this case)
• r = the annual interest rate (decimal)
• n = the number of times that interest is compounded per year
• t = the time the money is invested for, in years

In the given question, P = $2000, r = 2.8% or 0.028 (as a decimal), n = 4 (quarterly compounding), and t = 5 years.

We can calculate A as follows:

A = 2000(1 + 0.028/4)^(4*5)

A = 2000(1 + 0.007)^20

A = 2000(1.007)^20

A = 2000 * 1.148523...

A = $2297.05

The total amount in the account after 5 years, compounded quarterly at a 2.8% interest rate, will be approximately $2297.05.