Question

You can receive $400,000 ten years from today or $800,000 thirty years from today. What interest rate makes them equivalent ?

Answer 1

Present value-Future value/(1+interest rate)^Number of years

Present value of $400000 to be received 10 years from now will be:
Present value=400000/(1+r)^10

Present value of $800000 to be received 30 years from now will be:
Present value=800000/(1+r)^30

Equalizing the two equations, we get;

400000/(1+r)^10=800000/(1+r)^30

=>4/(1+r)^10=8/(1+r)^30
Multiplying, (1+r)^10 to both the sides, we get;
=>4=8/(1+r)^20
=>(1+r)^20=8/4   
=>(1+r)^20=2
=>1+r=2^(1/20)
=>r=2^(1/20)-1=0.035264924 or 3.53%

So, the interest rate that makes them equivalent is 3.53%