Answer:
a) To calculate the amount you will have in the account in 15 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the account
P = the initial deposit ($100)
r = the annual interest rate (4% or 0.04)
n = the number of times the interest is compounded per year (monthly, so n = 12)
t = the number of years (15)
Substituting the given values into the formula, we have:
A = 100(1 + 0.04/12)^(12*15)
Calculating this using a calculator or spreadsheet, we find that the future value of the account in 15 years is approximately $2,481.64.
b) To find the total amount of money you will put into the account, we can multiply the monthly deposit ($100) by the number of months in 15 years:
Total money deposited = $100/month * 12 months/year * 15 years
Calculating this, we find that the total money deposited is $18,000.
c) To find the total interest earned, we can subtract the total amount of money deposited from the future value of the account:
Total interest = Future value of the account - Total money deposited
Total interest = $2,481.64 - $18,000
Calculating this, we find that the total interest earned is approximately -$15,518.36.
Please note that the negative value for the total interest earned indicates that the amount withdrawn from the account is greater than the total deposits made. Double-check the calculations to ensure accuracy.
Explanation: