Final answer:
Samantha's n is the number of years she must wait until she starts receiving her perpetuity due payments. To find n, we need to determine the present value of her perpetuity due, which will be equal to half of the value Roger spent on his perpetuity, and then solve for n using the present value formulas for perpetuities due and deferred perpetuities.
Step-by-step explanation:
The question concerns the calculation of the number of years (n) Samantha must wait until starting to receive payments from a perpetuity due that she purchases with her share of the inheritance. A perpetuity due is a series of indefinite cash flows that occur at the beginning of each period. Samantha's perpetuity due has an annual payment of 308,961.6427, with the payments starting after n years and based on an annual effective interest rate of 5%.
To find the value for n, we can set up the equation to calculate the present value of Samantha's perpetuity due and solve for n, using the formulas for the present value of a perpetuity due and the present value of an nth year deferred perpetuity due. The value of the perpetuity due, according to the information given about Roger's transactions, should be equal to half of the value that Roger spent on his perpetuity since they split the inheritance equally. roger's perpetuity consists of two parts: a 20-year annuity due paying 60,000 and a perpetuity due paying 90,000 thereafter with a 4% effective annual rate. We need to calculate the present value of those two parts and sum them up to get the total value of the perpetuity Roger bought. By doing this, we find the amount that each sibling inherited and then use this value to find Samantha's n by equating it to the present value of a perpetuity due deferred for n years and solving for n.