a woman deposits $9000 at the end of each year for 7 years in an account paying 4%interest compounded annually
A = P(1+r)^t
To find the future value of the deposits, we can use the formula for compound interest:
FV = P(1 + r/n)^(nt)
Where:
FV = Future Value
P = Principal amount (the deposit amount)
r = Annual interest rate (in decimal form)
n = Number of times interest is compounded per year
t = Number of years
In this case, the principal amount (P) is $9,000, the annual interest rate (r) is 4% (0.04 in decimal form), and the deposits are made annually, so the number of times interest is compounded per year (n) is 1. The number of years (t) is 7.
Let's calculate the future value of the deposits:
FV = $9,000(1 + 0.04/1)^(1*7)
FV = $9,000(1 + 0.04)^7
FV = $9,000(1.04)^7
To find the future value, we can use a calculator or perform the calculation step by step:
FV = $9,000(1.04)(1.04)(1.04)(1.04)(1.04)(1.04)(1.04)
FV ≈ $11,580.87
Therefore, the future value of the deposits after 7 years, with an annual interest rate of 4% compounded annually, is approximately $11,580.87.