Question

I put $1000 of my savings in the bank account with a yearly interest rate of 10%. It means that every year 10% of the current amount in the account is added to it. What is the amount in the account in two years time?

Answer 1

The future value of $1000 deposited in a bank account with a 10% annual interest rate, compounded annually, after two years is $1210.

Step-by-step explanation:

The question involves calculating the future value of money when $1000 is deposited in a bank account with a yearly interest rate of 10%. We'll be using the formula for compound interest to determine the amount in the account after two years.

To calculate the total amount after two years with compound interest, we use the formula:

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

Where:

A is the amount of money accumulated after n years, including interest.

P is the principal amount (the initial amount of money).

r is the annual interest rate (decimal).

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

t is the time the money is invested or borrowed for, in years.

In this case, the principal amount P = $1000, the annual interest rate r = 10% or 0.10, the number of times interest is compounded per year n = 1 (since it is compounded annually), and the time t = 2 years.

Substituting these values into the formula gives us:

A =
`1000(1 + 0.10/1)^((1 X 2))`

After simplifying, we get:

A =
`1000(1 + 0.10)^2`
A =
`1000(1.10)^2`
A = 1000(1.21)

So, the total amount after two years is:

A = $1210

The interest compounded annually at a 10% rate on a $1000 deposit will result in a balance of $1210 after two years.

Answer 2

After two years, with a 10% annual compound interest rate, the amount in the bank account grows to $1210.

Step-by-step explanation:

Calculating Compound Interest

To calculate the total amount in the bank account after two years with a yearly interest rate of 10%, we use the formula for compound interest, which is A = P(1 + r/n)^(nt), where:

• A is the amount of money accumulated after n years, including interest.
• P is the principal amount (the initial amount of money).
• r is the annual interest rate (in decimal).
• n is the number of times that interest is compounded per year.
• t is the time the money is invested or borrowed for, in years.

Since the interest is compounded annually, n will be 1. Our principal P is $1000, the annual interest rate r is 0.10, and the time t is 2 years.

Now, let's calculate the amount of money in the account after two years:

1. Convert the interest rate from percentage to decimal: 10% = 0.10
2. Substitute the values into the compound interest formula: A = 1000(1 + 0.10/1)^(1*2)
3. Calculate the amount: A = 1000(1.10)^2
4. Calculate the power: A = 1000 * 1.21
5. Finally, calculate the total amount: A = $1210

Therefore, the amount in the account after two years would be $1210.