Question

Determine the uniform series of payments that correspond to each condition and sketch a cash flow...

Determine the uniform series of payments that correspond to each condition and sketch a cash flow diagram.

  1. A present worth of $500 with an interest rate of 10% and payments in periods 1 through 5.
  2. A future value of $2000 in period 10 with an interest rate of 12% and payments in periods 1-10.
  3. A future value of $5000 in period 10 with an interest rate of 5% and payments only in periods 1-8.
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Answer #1

Uniform series of payments at regular intervals is known as Annuity

1)

Present Value = Annuity * Present Value of Annuity of $1(10%,5years)

500 = Annuity * 3.791

Annuity = 500 / 3.791

Annuity = $131.89

2)

Future Value = Annuity * Future Value of Annuity of $1(12%,10years)

$2,000 = Annuity * 17.549

Annuity = $2,000 / 17.549

Annuity = $113.967

3)

Firstly we shall compute future value of year 8 using Future value of year 10 by discounting the same

Future Value of year 8 = Future value of year 10 / [(1 + .05)^2]

Future Value of year 8 = $5000 / 1.1025

Future Value of year 8 = $4535.147

Future Value = Annuity * Future Value of Annuity of $1(5%,8years)

$4535.147 = Annuity * 9.549

Annuity = $4535.147 / 9.549

Annuity = $474.934

Note- It has been assumed that all payments are made at the end of year.

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