How much must you deposit in an account that pays 7% annual interest compounded yearly to have a balance of $550 after 5 years?
To determine the amount that you need to deposit in an account to have a balance of $550 after 5 years with an annual interest rate of 7% compounded yearly, you can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = the principal amount (the initial deposit)
r = the annual interest rate (expressed as a decimal)
n = the number of times that interest is compounded per year
t = the number of years
In this case, we want to find the principal amount (P). We know that A = $550, r = 7% (0.07 as a decimal), n = 1 (compounded yearly), and t = 5.
Plugging the given values into the formula, we can rearrange it to solve for P:
P = A / (1 + r/n)^(nt)
Let's calculate the principal amount:
P = $550 / (1 + 0.07/1)^(1*5)
P = $550 / (1 + 0.07)^5
P = $550 / (1.07)^5
P = $550 / 1.4025511
P ≈ $391.64
Therefore, you need to deposit approximately $391.64 in the account to have a balance of $550 after 5 years.