Question

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.

Answer 1

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