Answer: 105.11$
Step-by-step explanation:
To calculate the monthly deposit for Nicole's savings account, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where:
A = the amount of money in the account after t years
P = the principal amount (the initial amount of money deposited)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years
In this case, Nicole wants to save $4000 in 3 years. The interest rate is 4.2% per year, compounded monthly. We can use the formula above to calculate how much she needs to deposit at the end of each month:
A = 4000
P = ?
r = 0.042/12 = 0.0035 (monthly interest rate)
n = 12 (compounded monthly)
t = 3
4000 = P(1 + 0.0035)^36
P = 4000 / (1 + 0.0035)^36
P ≈ $105.11
So Nicole needs to deposit approximately **$105.11** at the end of each month to save $4000 in 3 years with an interest rate of 4.2% per year, compounded monthly.