Midterm 1 Constant Series Questions

For questions 1-3 consider the following:

Aunt Bill is a cigarette loving benefactor. Aunt Bill knows that you have a pack a day, \$150 per month, smoking habit and that you have access to an account that earns 1/2% per month. It is her intention to buy your cigarettes for the next 400 months.

1. How much would Aunt Bill have to deposit into the account now to fund your cigarette
purchases for the next 400 months?

(a) \$8,160.68
(b) \$25,919.66
(c) \$55,256.00
(d) None of the above

Solution:

Since the amount spent on smoking is a constant \$150 a month we know we are dealing with a constant series. From the problem statement we know N = 400 months and i = ½% = 0.005. Now that we know all the facts we need to compute the present worth.

P = \$150(P|A,i = 0.005,N = 400) = \$25,919.66

2. What if, immediately after Aunt Bill made this deposit you decided to quit smoking
and save the money until retirement. How much would be in the account when you
retire in 400 months?

(a) \$60,000.00
(b) \$25,919.66
(c) \$190,569.75
(d) None of the above.

Solution:

Since will not be smoking any of Aunt Bill’s deposit, we take the initial deposit and determine its future value in 400 months at an interest rate of ½%. F = \$25,919.66(F|P,i = 0.005,N = 400) = \$190,569.75.

3. What if Aunt Bill wanted to spread those deposits over the next year as 12 equal sized
deposits, starting not this month but next, i.e., month one not month zero . How much
would she deposit each month to fund those cigarette purchases?

(a) \$2,159.97
(b) \$5,000.00
(c) \$2,230.81
(d) None of the above

Solution: