Darren is 30 and is debating whether he should start investing $100 a month now for retirement at 60 or if he should wait until he is more established at 40 and invest $200 a month then. if the investment earns approximately 10% p. a. compounded monthly, what would you recommend for saving the largest amount? provide supporting evidence for your decision and indicate the values for any parameters used in calculations.

Hi there
The formula of the future value of annuity due because you invest now means you invest at the beginning of each month

Fv=pmt [(1+r/k)^(kn)-1)÷(r/k)]×(1+r/k)
The first option you invest 100 at the beginning of each month for 30 years (60-30) therefore
Fv=100×1+0.1÷12)^(12×30)
−1)÷(0.1÷12))×(1+0.1÷12))
=227,932.53...is higher

The second option you invest 200 at the beginning of each month for 20 years (60-40) therefore
Fv=200×1+0.1÷12)^(12×20)
−1)÷(0.1÷12))×(1+0.1÷12))
=153,139.38...is lower

So I would choose the first option which is invest 100 due to higher amount

Hope it helps