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Understanding Joint Impact: How Changes in Interest Rates and Account Size Affect Payments

This article explores the concept of joint impact as it relates to financial payments, particularly focusing on the effects of simultaneous changes in interest rates and account size. It breaks down how different factors, such as a higher interest rate and an increased account size, jointly affect payment amounts. By explaining key equations, the article delves into the implications of these changes and presents potential solutions for allocating the joint impact. It serves as a guide for understanding the financial dynamics involved in such scenarios.

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Understanding Joint Impact: How Changes in Interest Rates and Account Size Affect Payments

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Presentation Transcript

  1. Dealing with the Joint ImpactDad Pays But doesn’t know how much Ted Mitchell

  2. The problem of how much • Should Dad pay • Was solved for a improved partial performance when you got a higher interest rate • We measured the impact that the difference in the interest rate had on the difference in the interest payments

  3. I∆R = min(A1,A2) x ∆R I∆R = $200 x 1% = $2 Interest rate I∆A = min(R1,R2) x ∆A I∆A = 4% x -$300 = -$12 5% ∆R = 1% 4% $200 Account size $500 ∆A = -$300

  4. What happens when both the things change in the same direction! Interest rate 5% ∆R = 1% 4% $200 Account size $500 ∆A = -$300

  5. If Both Changes are in the • Same Direction (+ or –) • Then the entire problem changes • Your bank account increases (not decreases) from $200 to $500 • ∆A = + $300 • Your interest rate increases by ∆r = 1% • Your interest payment increases by ∆Z = ($25 - $8) = $17

  6. Interest rate 5% 4% Old Payment of 4% x $200 = $8 $200 Account size $500 ∆A = -$300

  7. The new payment is 5% x $500 = $25 Interest rate 5% ∆R = 1% 4% $200 Account size $500 ∆A = -$300

  8. The new payment is 5% x $500 = $25 Interest rate 5% ∆R = 1% 4% Old Payment of 4% x $200 = $8 $200 Account size $500 ∆A = -$300

  9. Start Again: $200 account that grows

  10. The total new payment is 0.05 x $500 = $25 Interest rate 5% Impact of ∆R =$2 J =$3 ∆R = 1% 4% Old Payment of $8 Impact of the ∆A = $12 $200 Account size $500 ∆A = -$300

  11. The $3 is a Joint impact Now the $3 is here it does exist! Interest rate 5% ∆R = 1% 4% $200 Account size $500 ∆A = -$300

  12. The $3 is here as a joint impact! An Interaction term A synergy term Interest rate 5% ∆R = 1% 4% $200 Account size $500 ∆A = -$300

  13. It is the result of both changes together! Interest rate 5% Joint ∆R = 1% 4% $200 Account size $500 ∆A = -$300

  14. The Total Impact Equation • ∆Z = I∆A + I∆R + J • Change in the payment, ∆Z = (the Impact of the Difference in the size of the Account, I∆A) + • (the Impact of the Difference in the Interest Rate, I∆R) + • (the Joint Impact (if any), J, of the differences in the two factors.)

  15. The total new payment is $25 Interest rate 5% Impact of ∆R =$2 J =$3 ∆R = 1% 4% Payment of $8 Impact of the ∆A = $12 $200 Account size $500 ∆A = -$300

  16. How should the $3 due to joint impact • Be allocatedThree possible solutions: • 1) All to the difference in account size? • 2) All to the difference in interest rate? • 3) Split it in half • 4) Split proportionately between the two factors? • Accountants favor solutions #1 & #2 • Marketing Managers favor solution #4

  17. Any questions on the Joint Impact or Synergy created with simultaneous changes in the factor’s that determine a machines performance?

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