Her has $1500 in a retirement account earning 5% interest compounded annually. Each year after the first, she makes and additional deposits of $1500. After 5 years , what was her account balance if she did not make any withdrawals?
amount
= 1500 + 1500(1.05^4 - 1)/.05
= 7965.19
To calculate her account balance after 5 years, we need to use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final account balance
P = the initial principal (starting amount)
r = annual interest rate (in decimal form)
n = number of times interest is compounded per year
t = number of years
In this case, her initial principal (P) is $1500, the annual interest rate (r) is 5% or 0.05, and interest is compounded annually (n = 1). She makes additional deposits of $1500 each year, but since she didn't specify the timing of the deposits, we will assume they are made at the end of each year.
Now let's calculate her account balance after 5 years:
Step 1: Calculate the balance after the first year.
A1 = P(1 + r/n)^(nt)
A1 = $1500(1 + 0.05/1)^(1*1)
A1 = $1500(1 + 0.05)^1
A1 = $1500(1.05)
A1 = $1575
Step 2: Calculate the balance after each subsequent year, including the additional deposits.
A2 = (A1 + $1500)(1 + 0.05/1)^(1*1)
A2 = ($1575 + $1500)(1 + 0.05)^1
A2 = $3075(1.05)
A2 = $3228.75
A3 = ($3228.75 + $1500)(1 + 0.05/1)^(1*1)
A3 = ($4728.75)(1.05)
A3 = $4965.1875
A4 = ($4965.1875 + $1500)(1 + 0.05/1)^(1*1)
A4 = ($6465.1875)(1.05)
A4 = $6793.446875
A5 = ($6793.446875 + $1500)(1 + 0.05/1)^(1*1)
A5 = ($8293.446875)(1.05)
A5 = $8708.114219
Therefore, after 5 years, her account balance, without making any withdrawals, would be approximately $8708.11.