Meg opens a savings account by depositing $10,000. The annual interest, r, is compounded monthly. At the end of the second month, $5,000 is added. At the end of the fourth month, $2000 is added. (Nothing is added at the end of the first of third month).
Write an expression for the balance in th account at the end of the fourth month, using x to represent the multiplier (1+r/12)

Question

Meg opens a savings account by depositing $10,000. The annual interest, r, is compounded monthly. At the end of the second month, $5,000 is added. At the end of the fourth month, $2000 is added. (Nothing is added at the end of the first of third month).
Write an expression for the balance in th account at the end of the fourth month, using x to represent the multiplier (1+r/12)

barrycarter · Answer

Start: 10000

End of month 1: 10000x [1 month worth of interest on $10K]

End of month 2: 10000x^2 + 5000 [5K new + 2 months interest on 10K]

End of month 3: (10000x^2+5000)*x [interest on month 2 balance]

End of month 4: (10000x^2+5000)*x*x + 2000 [2K new + interest on month 3 balance]

Simplifying the above:

10000*x^4 + 5000*x^2 + 2000

laurena · Answer

Thank you!