Suppose you deposit $2,000 in a savings account that pays interest at an annual rate of %6. If no money is added or withdrawn from the account, answer the following questions.
How much will be in the account after 4 years?
To determine the amount in the account after 4 years, we need to calculate the interest earned and add it to the initial deposit.
The annual interest rate is 6%, which can be written as a decimal as 0.06.
Using the formula for compound interest, the amount in the account after 4 years is given by:
A = P(1 + r/n)^(nt)
Where:
A = the amount in the account after 4 years
P = the initial deposit ($2,000)
r = the annual interest rate (0.06)
n = the number of times interest is compounded per year (assuming it is compounded annually, n = 1)
t = the number of years (4)
Plugging in the values into the formula, we get:
A = 2000(1 + 0.06/1)^(1*4)
A = 2000(1 + 0.06)^4
A = 2000(1.06)^4
A ≈ 2000 * 1.26248
So, after 4 years, there will be approximately $2,524.96 in the account.