Question

A rich woman would like to leave $10000 a year, starting 1 year from now, to be divided equally among all her descendants. she puts no time limit on this bequeathment and is able to invest for this long-term outlay of funds

QUESTION 1

how much must she invest now to meet such a long term commitment if she is able to invest for this long-term outlay of funds at 2.5% compounded anually?

QUESTION 2

how much must she invest now to meet such a long term commitment if she is able to invest for this long term outlay of funds at 2.5% compounded semi-anually?

ROUND ANSWERS TO THE NEAREST INTEGER!!!

INCLUDE ALL DECIMALS FROM YOUR CALCULATOR UNTILL YOU OBTAIN THE FINAL ANSWER FOR EACH QUESTION.!

help please!

Answer 1

a.

Amount of annuity required forever (P)= 10000 a year

Amount is starting from end of year 1.

Interest rate compounded annually is 2,5%. so interest rate per period (i) = 2.5%

Present value of perpetuity = P/i

=10000/2.5%

=400000

So She must invest $400000 now to meet such a long commitment.

b.

Interest rate compounded semiannally (r) =2.5%

Number of compounding in year (m) =2

Effective annual rate =((1+(r/m))^m)-1

=((1+(2.5%/2))^2)-1

=0.02515625

Present value of perpetuity = P/i

=10000/0.02515625

=397515.53

So She must invest $397515.53 now to meet such a long commitment.