Suppose that $3,000 is placed in an account that pays 8% interest compounded each year assume that no withdrawals are made from the account find the amount in the account at the end of one year
The amount in the account at the end of one year can be found using the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the amount of money accumulated after n years, including interest.
P = the principal amount (the initial amount of money)
r = annual interest rate (in decimal form)
n = number of times that interest is compounded per year
t = the time the money is invested for, in years.
In this case, P=$3000, r=8% or 0.08 (in decimal form), n=1 (since interest is compounded once per year), and t=1 year.
Plugging these values into the formula gives:
A = $3000(1 + 0.08/1)^(1*1)
A = $3000(1.08)^1
A = $3000 * 1.08
A = $3240
So, there would be $3240 in the account at the end of one year.
To find the amount in the account at the end of one year, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the amount in the account at the end of one year
P = the principal amount (initial deposit)
r = annual interest rate (as a decimal)
n = number of times interest is compounded per year
t = number of years
In this case:
P = $3,000
r = 8% = 0.08 (as a decimal)
n = 1 (compounded once per year)
t = 1 (one year)
Substituting these values into the formula:
A = 3000(1 + 0.08/1)^(1*1)
Simplifying:
A = 3000(1 + 0.08)^1
A = 3000(1.08)
A = $3,240
Therefore, the amount in the account at the end of one year is $3,240.