An aggressive stockbroker claims an ability to consistently earn 12% per year on an investor’s money. A client invests $10,000 now, $30,000 three years from now, and $8000 per year for 5 years starting 4 years from now. (a) How much money can the client withdraw every year forever, beginning 20 years from now? (b) What is the capitalized cost of the client’s investments if the $8000 per year is expected to continue for an unspecified time into the future?
What will be an ideal response?
(a) Find future value in year 19, then multiply by i
F19 = 10,000(F/P,12%,19) + 30,000(F/P,12%,16) + 8000(F/A,12%,5)(F/P,12%,11)
= 10,000(8.6128) + 30,000(6.1304) + 8000(6.3528)(3.4785)
= $446,826
A = 446,826(0.12)
= $53,619 per year (forever)
(b) CC = -10,000 – 30,000(P/F,12%,3) – (8000/0.12)(P/F,12%,3)
= -10,000 – 30,000(0.7118) – 66,667(0.7118)
= $-78,808
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