Math  /  Numbers & Operations

QuestionTom deposits $2400\$ 2400 in an account that pays 2.2%2.2 \% simple interest. He keeps the money in the account for 2 years without any deposits or withdrawals. How much is in the account after 2 years?

Studdy Solution

STEP 1

1. The principal amount deposited by Tom is $2400 \$2400 .
2. The annual simple interest rate is 2.2% 2.2\% .
3. The time period for which the money is kept in the account is 2 2 years.
4. No additional deposits or withdrawals are made during this period.

STEP 2

1. Define the formula for simple interest.
2. Calculate the simple interest earned over the period.
3. Calculate the total amount in the account after 2 years.

STEP 3

The formula for simple interest is given by:
I=P×r×tI = P \times r \times t
where I I is the interest, P P is the principal amount, r r is the annual interest rate (in decimal), and t t is the time in years.

STEP 4

Convert the interest rate from a percentage to a decimal:
r=2.2100=0.022r = \frac{2.2}{100} = 0.022

STEP 5

Substitute the values into the simple interest formula to find the interest earned:
I=2400×0.022×2I = 2400 \times 0.022 \times 2

STEP 6

Calculate the interest:
I=2400×0.022×2=105.6I = 2400 \times 0.022 \times 2 = 105.6

STEP 7

Calculate the total amount in the account after 2 years by adding the interest to the principal:
A=P+I=2400+105.6A = P + I = 2400 + 105.6

STEP 8

Calculate the total amount:
A=2400+105.6=2505.6A = 2400 + 105.6 = 2505.6
The total amount in the account after 2 years is:
$2505.60\boxed{\$2505.60}

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