Question

Derek will deposit $3,269.00 per year for 13.00 years into an account that earns 8.00%. Assuming the first deposit is made 6.00 years from today, how much will be in the account 32.00 years from today?

Answer 1

Hi

Since first deposit is made 6 years from today and for 13 years.

Hence at first we will calculate future value of investment at the end of deposit that means at end of 13+6 = 19 years

So Future value of deposit at end of 19 years = (C/r)*((1+r)^t-1)

Here C = $3,269

time t = 13 years

rate r = 8%

So Future value at end of 19 years or the beginning of 20th year= (3269/0.08)*(1.08^13-1)

=40862.5*1.7196

=$70,268.12

Now We will want the value of account in 32 years

then time t = 32 -20 = 12 years

rate r = 8%

P= $70,268.12

F = P*(1+r)^t

= 70268.12*(1+8%)^12

=70268.12*2.518

=$176,947.09

Hence the amount in 32 years will be $176,947.09

Thanks