Advanced Algebra

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Advanced Algebra

• Lesson 1-5
• Pg. 57

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Use recursive formula for loans and investments

• For both loans and investments , with regular
  payments or deposits of a fixed amount the
  sequence of balances is generated by the
  recursive rule.
• The recursive
  equation will be in this form.
• 1) The value of r is 1 more than the interest
  rate being calculated at the time.
• 2) For loans, d is negative. For investments, d
  is positive.
• 3) The principal, or initial amount of the loan
  or investment, is given by .

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Investigation from Pg. 62

• You plan to borrow 22,000 to purchase a new car.
  The investment must be paid off in 5 years (60
  months). The bank charges interest at an annual
  rate of 7.9 compounded monthly. Part of each
  monthly payment is applied to the interest , and
  the remainder reduces the starting balance, or
  principal.
• Borrow 22,000 for a new car.
• Pay off in 5 years (60 months)
• Annual interest rate 7.9, compounded monthly.

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Investigation Continued

• What is the monthly interest rate?
• Interest rate 1.006583
• Record the balances for the 1st six months if we
  make a monthly payment of 300.
• 300-144.83 155.17 300 payment
• 
  144.83 Interest
• 
  155.17 amt. paid on loan

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Investigation Continued

• Plug the formula into calculator.

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Investigation Continued

• How many months would it take to pay off this
  loan by making 300 a month payments? Ans.
  101 months
• What monthly payment allows you to pay off loan
  in 60 months? Ans. 445.03
• Using your calculator to get these answers.
• Go to apps on calculator
• Go to Finance, hit enter.
• Go to TVM solver, hit enter.

7

• N number of months
• I Annual interest rate as a .
• PV The principle or starting value
• PMT The payment
• FV Final value
• P/Y Payments per year
• C/Y Interest calculations per year
• PMT End Begin Indicates whether payments are
  made at the beginning or end of the month. After
  entering the six known values, highlight the
  value you want to find and press ALPHA then
  ENTER.

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Example

• UO 146,000 Principle
• 7.25 annual interest rate
• 30 year loan 360 months
• What is the monthly payment?
• How much will you pay over the life of the loan?

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• Example cont.
• 360(995.98) 358,552.80
• Example 2 Pg. 63
• Gwens employer offers an investment plan that
  invests a portion of each paycheck before taxes
  are deducted. Gwen gets paid every week. The plan
  has a fixed annual interest rate of 4.75,
  compounded weekly, and she decides to contribute
  10 each week. What will Gwens balance be in 5
  years?

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Example 2 cont.

• Balance in 5 years 260 weeks.
• Go to y and put recursive formula in
  calculator.
• Then go to main screen. u(260) 2945.90
• If you use Finance Solver be sure to change P/Y
  to 52 and C/Y to 52. Also change N to 261.

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Assignment

• Pg. 64 1-7b all