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ohaa [14]
3 years ago
14

Tometeo wants to have $50,000 saved 15 years from now. How much must he deposit every month into an account that pays 2.8% inter

est, compounded monthly?
Mathematics
1 answer:
kotykmax [81]3 years ago
3 0

Answer:

  • $223.84 at the end of the month, or
  • $223.31 at the beginning of the month

Step-by-step explanation:

The annuity formula is used for this.

  A = P((1+r/12)^(12t) -1)/(r/12)

gives the balance A resulting from payments P being compounded monthly at annual rate r. (Payments are made at the end of the month.)

  50,000 = P((1 +.028/12)^(12·15) -1)/(0.028/12) ≈ 223.378772P

  P ≈ 50,000/223.378772 ≈ 223.84

To achieve the desired balance, Tometeo must deposit $223.84 at the end of every month.

_____

If Tometeo makes his deposits at the beginning of the month, then the amount is less by the interest earned for the month:

  $223.84/(1 +.028/12) ≈ $223.31 . . . . beginning of the month deposit amount

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Answer:

a) 8.13

b) 4.10

Step-by-step explanation:

Given the rate of reaction R'(t) = 2/t+1 + 1/√t+1

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On integrating R'(t)

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When t = 1

R(1) = 2ln2 + 2√2

≈ 4.21

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R(12) = 2ln13 + 2√13

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≈ 8.13

Total reactions to the drugs over the period from t = 1 to t= 12 is approx 8.13.

b) For total reactions from t = 12 to t = 24

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R(24) = 2ln25 + 2√25

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*see attachment for the figure referred to

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