Answer to Question #89846 in Financial Math for BUTT

Question

If an employee deposits Rs. 2,000 at the end of each year into his company’s plan which pays 7% interest compounded quarterly, how much will he have in the account at the end of 5 years?

Answer 1

Let number of years = n = 5, annual interest = r = 7% = 0.07, number of compounds = m = 4, deposit = R = 2000.

Value A_k of deposit R after k years A_k = R*(1+r/m)^k*m.

Future value of the first deposit A_n = R*(1+r/m)^n*m

Future value of the second deposit A^n-1 = R*(1+r/m)^(n-1)*m

.......

Future value of the last deposit A₀= R*(1+r/m)^0*m

S = A₀ + A₁ + .. + An = R*(1+r/m)^0*m+ R*(1+r/m)^1*m+... + R*(1+r/m)^n*m =

(this is sum of geometric series with ratio = (1+r/m)^m )

=R*( (1+r/m)(^n+1)*m-1 )/( (1+r/m)^m-1 )

S = 2000( (1+0.07/4)^6*4-1 )/( (1+0.07/4)⁴-1 ) = 14373.7753523

Answer: 14373.7753523