The HBO co. is raising \$150,000 in 30 months by making monthly deposits which can be invested at 6%(12). Assuming they withdraw \$150,000 a month after the last deposit.
If they deposit \$R per month for the first 10 months, \$2R for the next 10 months and \$3R for the last 10 months, what is R?
If they deposit \$3R during the first 10 months, then \$2R during the second 10 months and \$R during the last 10 months, what is this time R?
What is the reason of the difference in the answers of a. and b.?
I'm using the formula r = (s_ni)/[(1+i)^n-1] = (150,000(.06/12))/[(1+(.06/12)^10-1)]=14,665.59 but i don't think this is right.
HINT
(1) and (2) are just mechanical - compute the sums that accrue for each of the deposits, you get 3 geometric series.
for (3), the interest accrues differently. Thinmk about it on this simplified example. Would you prefer a bank account in which I deposit \$1 first and \$2 in a year, or the one with \$2 first and \$1 in a year?