Problema Solution
In order to accumulate enough money for a down payment on a house, a couple deposits $210 per month?
into an account paying 6% compounded monthly. If payments are made at the end of each period, how much money will be in the account in 4 years? (round to the nearest dollar)
Answer provided by our tutors
S = 210 * (1 + 0.06/12) + 210 * (1 + 0.06/12)^2 + .... + 210 * (1 + 0.06/12)^48
S = 210 * 1.005 + 210 * 1.005^2 + ... + 210 * 1.005^48
S = 210 * 1.005 * (1 + 1.005 + 1.005^2 + ... + 1.005^47)
S * 1.005 = 210 * 1.005 * (1.005 + 1.005^2 + ... + 1.005^47 + 1.005^48)
S * 1.005 - S = 210 * 1.005 * (1.005 + 1.005^2 + ... + 1.005^47 + 1.005^48 - 1 - 1.005 - ... - 1.005^47)
S * (1.005 - 1) = 210 * 1.005 * (1.005^48 - 1)
S * 0.005 = 210 * 1.005 * (1.005^48 - 1)
S = 210 * 1005 * (1.005^48 - 1) / 5
S = 210 * 201 * (1.005^48 - 1)
S = 11417.347489836361011406410440876