Question

(a) Suppose that you can invest with a continuously compounded rate of 5.25% per annum.

(i) If you invest $50,000 today, how many years will it take for your investment to be worth $1 million?

(ii) If you want your investment to grow to be $1 million in 10 years, how much do you need to invest today?

(iii) Compute the equivalent effective 1-year rate

Answer 1

i)
Number of years can be calculated by using the following excel formula:
=NPER(rate,pmt,pv,fv)
=NPER(5.25%,0,-50000,1000000)
= 58.55 Years

Number of years = 58.55 years

ii)
Present value can be calculated by using the following excel formula:
=PV(rate,nper,pmt,fv)
=PV(5.25%,10,0,-1000000)
= $599,485.88

The amount you need to invest today = $599,485.88

iii)
Equivalent effective 1 year rate = e^0.0525 - 1
= 1.0539 - 1
= 5.39%