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Nicole wants to save $4000 for a backpacking trip through Europe when she finishes college in 3 years. Interest on her savings account is 4.2%, compounded monthly. How much does she need to deposit at the end of each month? (4 marks)

1 Answer

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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.
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