Question

A savings account pays 2% interest compounded annually. If $1,200 is deposited initially and again at the first of each year, how much money will be in the account three years after the initial deposit?
A)$2,472.48
B)$3,672.48
C)$3,745.93

Answer 1

if anyting we can brute math it

Answer 2

if we start with a principal amount of P, after 1 year we have

P + P(r)


after 2 years we have

P + P(r) + ( P + P(r))r


after 3 years we have

P + P(r) + ( P + P(r))r + (P + P(r) + ( P + P(r))r)r

Answer 3

when we simplify this we get

P + Pr + ( P + Pr)r + (P + Pr + ( P + Pr)r)r

P + Pr + Pr + Prr + (P + Pr + Pr + Prr)r

P + Pr + Pr + Prr + Pr + Prr + Prr + Prrr

P(1 + r + r + rr + r + rr + rr + rrr)

P(1 + 3r + 3rr +rrr)

P(1+r)^3