Suppose Jessica places in an account that pays interest compounded each year.
Assume that no withdrawals are made from the account.
Follow the instructions below. Do not do any rounding.
a)Find the amount in the account at the end of 1 year.
b) Find the amount in the account at the end of 2 years.
To find the amount in the account at the end of 1 year, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount in the account
P = the initial amount (principal)
r = the annual interest rate (expressed as a decimal)
n = the number of times interest is compounded per year
t = the number of years
In this case, since no withdrawals are made, the final amount in the account is equal to the initial amount plus the interest earned:
A = P + I
a) To find the amount in the account at the end of 1 year:
Let's assume that Jessica places $1000 in the account and the interest rate is 5% per year, compounded annually. Plug in the values into the formula:
P = $1000
r = 0.05
n = 1 (compounded annually)
t = 1 year
A = $1000(1 + 0.05/1)^(1*1)
= $1000(1 + 0.05)^1
= $1000(1.05)
= $1050
Therefore, the amount in the account at the end of 1 year is $1050.
b) To find the amount in the account at the end of 2 years:
We can use the same formula, plugging in the values:
P = $1050 (the amount in the account after 1 year)
r = 0.05
n = 1
t = 2 years
A = $1050(1 + 0.05/1)^(1*2)
= $1050(1 + 0.05)^2
= $1050(1.05)^2
= $1102.50
Therefore, the amount in the account at the end of 2 years is $1102.50.
Recall that the amount after t years is
A = P(1+r)^t