Futurama

Math answers

1. 2999 - 1999 = 1000. Fry was only in suspended animation for 1000 years not 1,000,000.
2. Substitution problem. Use the formula P = A/(1+i)ⁿ. A is the future value. i = the interest. n is the number of years, and P = the present value. A = 4,300,000,000. i = 0.0225. n = 1000.
   P = 4,300,000,000/(1 + .0225)¹⁰⁰⁰
   P = 4,300,000,000/(1.0225)¹⁰⁰⁰
   P = 4,300,000,000/4,605,923,064.206
   P = 0.93 rounded to the nearest cent.
3. The interest is cut in half, and the time is doubled when interest is compounded semiannually.
   P(1 + i)ⁿ = A becomes $0.93(1 + .01125)²⁰⁰⁰ = A
   $0.93(1.01125)²⁰⁰⁰ = A
   $0.93( 5212778131.082) = A
   $4,847,883,661.91 rounded to the nearest cent.
4. The interest is divided by 4, and the time is multiplied by 4 when interest is compounded quarterly.
   P(1 + i)ⁿ = A becomes $0.93(1 + .005625)⁴⁰⁰⁰ = A
   $0.93(1.005625)⁴⁰⁰⁰ = A
   $0.93( 5549396710.815) = A
   $5,160,938,941.06 rounded to the nearest cent.
5. $120. Bender receives $1200 for 12 children. 12 * $100 = $1200. Bender spends $1320 for 12 children. 12 * $110 = $1320. Bender looses $120. $1320 - 1200 = $120. Bender spends more than he receives which generates a loss.