Q1d and Q1e) You can assume that Sheryl receives the first payment on the last day of her 67th year and the final payment on the last day of her 85th year. This means she receives payments at the end of her 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, and 85 years. This is a total of 19 years that she will receive payments under Plan D (you can use the same concept to calculate the answers for Q 1a, Q 1b, and Q 1c). Under Plan D, for the first 3 years she will receive annual payments of $12,000 and for the next 16 years she will receive annual payments of $29,760.
Q 2d) Plan D: To make the computation easier you may use the following hint:
Assume that Sheryl will receive annual payments of $29,760 for all of the 19 years i.e. A = $29,760 for all 19 years.
To adjust for the extra payment (i.e. 29,760 - 12,000) she receives in the first 3 years, assume that Sheryl pays back $17,760 at the end of years 1, 2 and 3 respectively.
For the annual income convert $29,760 into FW using (F/A, 6%, 19).
For the amount paid back at the end of year 1 convert $17,760 into FW using (F/P,6%,18) as the gap between this time (i.e end of first year) and the end of time horizon (i.e. end of 19th year) is 18 (i.e. = 19 - 1).
For the amount paid back at the end of year 2 convert $17,760 into FW using (F/P,6%,17) as the gap between this time (i.e end of second year) and the end of time horizon (i.e. end of 19th year) is 17 (i.e. = 19 - 2).
And so on for the amount paid back at the end of year 3.
