Midterm 3 Review

1
Midterm 3 Review

• Sections 5.3-5.4

2
Geometric Series

• Find the sum of a geometric series of 15 terms
  with first term 6 and common ratio 3.
• We can use the formula
• with n 15, a 6, and ? 3.
• Then we get

3
Geometric Series

• Find the sum
• This is a geometric series with n 10, a 3,
  and ? 1/2.
• So the total is

4

• Bill wants to pay off the remainder of a loan.
  He still owes 10 quarterly payments of 200 each.
  If the interest on the loan is 8.4 compounded
  quarterly, how much does he need to pay now to
  pay off the loan? (Assume the payments are due
  at the beginning of the quarter.)
• We want to find the present value of an annuity
  due with R 200, r .021, and n 10.
• Using , we get

5

• You deposit 50 per month at the beginning of the
  month for the next two years. If the bank pays
  you 4.8 interest compounded monthly, how much
  will you have at the end of the two years?
• We use the formula for the future value of an
  annuity due with R 50, r .004, and n 24.
• Then

6

• A bank offers an annuity consisting of biweekly
  payments of 1200 for 20 years. If the bank pays
  6.5 interest compounded biweekly, how much
  should you pay for the annuity? Assume that
  payments are made at the end of the 2 weeks.
• We want to find the present value of an ordinary
  annuity.
• Using with R 1200, r .0025,
  and n 520, we get

7

• The Business College plans to set up a sinking
  fund to replace computers in the lab in 5 years.
  Their goal is to have 280,000. If they can get
  7.8 interest compounded quarterly on their
  money, how much should they put aside each
  quarter to meet their goal? (The deposits are
  made at the beginning of the quarter.)
• We want to find the future value of an annuity
  due.

8
Lottery Winners

• The 8 meat-packing plant workers in Nebraska
  recently won a lottery prize reported at 365
  million (paid out in monthly payments over 30
  years).
• What is the monthly payment?
• The cash payout (present value) of the jackpot is
  177.3 million.
• What interest rate is the lottery commission
  paying?
• Use the TVM solver

9

• A debt of 12,000 is to be repaid by quarterly
  payments of 2500 each, with 5.5 interest
  compounded quarterly. Fill in the amortization
  schedule below to find the amount still due at
  the beginning of the second year.
• Our periodic rate is .055/4 .01375

165.00
2335.00
2500
132.89
9665.00
2367.11
2500
100.35
2399.65
7297.89
2500
67.35
2432.65
4898.24
2465.59