Question

A savings account earns 6% (APR) interest calculated monthly, paid into the account at the end of 6 months. Travis deposits $100 into the account at the beginning of the first month. At the end of each month, he deposits an additional $100 into the account. How much interest will Travis have earned after 6 months?

Answer 1

The monthly increase can be written as a multiplier = 100%+6% = 106% = 1.06

End of month 1 = 100×1.06 = 106

Beginning of month 2 = 106+100 = 206
End of month 2 = 206×1.06 = 212

Beginning of month 3  = 212+100 = 312
End of month 3 = 312×1.06 = 330.72

Beginning of month 4 = 330.72+100 = 430.72
End of month 4 = 430.72×1.06 = 455.8

Beginning of month 5 = 555.8
End of month 5 = 555.8×1.06 = 589.148

Beginning of month 6 = 689.148
End of month 6 = 689.148×1.06 = 624.49688

The amount of interest Travis will receive at the end of month 6 is
624.49688 - 600 = 24.49688 ≈ $24.50