Question

Your finance advisor offers you an investment that promise $200 000 in 15 years from now. He said that you will need to contribute an initial investment of $45,000 now. Required:

a. What rate of interest was used in the computation of this investment offer assuming the rate is compounding annually?

b. If you wish to retire in just 10 years with the same $200 000 and the rate of return is 12%, how much money would you need to invest now?

c. If you wish to retire with $250 000, using the same initial investment of $45 000 and the rate of return of 15%, how long will you need to wait before you can retire?

Answer 1

a.

Present value = 45000

future value = 200000

Number of years (n) =15

Rate of return = ((future value/Present value)^(1/n))-1

=((200000/45000)^(1/15))-1

=0.1045562366 or 10.46%

So rate of return required is 10.46% compounded annually.

b.

Future value = 200000

Rate of return (i) =12%

Number of years (n) = 10

Present value = Future value/(1+i)^n

=200000/(1+12%)^10

=64394.64732

So amount need to invest now is $64394.65

c.

Amount invested Present value =45000

Future value required = 250000

Rate of return (i) =15%

Future value = Present value*(1+i)^n

250000=45000*(1+15%)^n

We will calculate n by trial and error method

assume n = 12 years

future value = 45000*(1+15%)^12

=240761.2547

assume n = 12.5 years

future value = 45000*(1+15%)^12.5

=258187.6818

we will calculate n by interpolation formula

interpolation formula = uper n -( uper n- lower n)*(Uper n value - Actual n value)/(uper n value- lower n value)

12.5 -( (12.5-12)*(258187.6818-250000)/(258187.6818-240761.2547))

=12.26507859 or 12.27 years

So you need to wait 12.27 years before you retire