In factored form, we have: A_1 = P + Pr = P(I + r). At the end of the second yea
ID: 3034879 • Letter: I
Question
In factored form, we have: A_1 = P + Pr = P(I + r). At the end of the second year the amount accumulated is A_2 = (P + Pr) + (P + Pr)r. Write an expressions for A_2 in factored form similar to that for A_1. Write an expression for the amount accumulated in three years, A_3 in factored form. Write an expressions for A, the amount accumulated in n years. Use the formula you developed in part c, and your calculator to find the amount accumulated if $10,000 is invested at 6 % and compounded annually for 20 years.Explanation / Answer
A.
Amount after 1 year = P + Pr = P*(1 + r)
Amount after two year = (P + Pr) + (P + Pr)*r = P*(1 + r)^2
B.
Amount after three year = P*(1 + r)^2 + P*(1 + r)^2*r = P*(1 + r)^3
C.
Similarly amount after n years
An = P*(1 + r)^n
D.
P = 10000
r = 6% = 0.06
n = 20 yrs
A = 10000*(1 + 0.06)^20 = $32071.35