Beatrice decides to deposit $100 per month at the end of every month in a bank with an annual interest rate of 5.5% compounded monthly . how much will she accumulate in her account after 4.5 years

We have to calculate a monthly annuity.

Total = Monthly Amount * [(1 + rate)^(n + 1) -1] / [rate] - Monthly Amount

where "n" is the number of compounding periods per year.
and n = 4.5*12 = 54
rate = rate/n = .055 / 12 = 0.0045833333

Total = 100 * [(1.0045833333)^55 -1] / [ 0.0045833333 ] -100
Total = 100 * 0.2859624157 /  [ 0.0045833333 ] -100
Total = 28.59624157 / [ 0.0045833333 ] -100
Total = 6,239.18 -100
Total = 6,139.18

Source:
http://1728.org/annuity3.htm  formula
http://1728.org/annuitym.htm calculator

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