Annuities and Gradients - Worked Examples

Example 1 — Present worth of PHP 100,000 paid at each year-end for 5 years at 8%.

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Example 2 — Annual payment equivalent to PHP 1,000,000 today over 8 years at 10%.

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Example 3 — Future worth of PHP 80,000 deposited annually for 6 years at 7%.

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Example 4 — Annual sinking-fund deposit needed for PHP 2,000,000 in 10 years at 6%.

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Example 5 — Present worth of a 5-payment annuity due of PHP 120,000 at 9%.

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Example 6 — Deferred annuity: PHP 200,000 at years 4 through 8, with i = 8%.

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Example 7 — Identify the arithmetic gradient in PHP 500k, 560k, 620k, 680k over years 1–4.

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Example 8 — Present worth of the standard arithmetic gradient 0, 50k, 100k, 150k, 200k at 10%.

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Example 9 — Present worth of PHP 300k, 340k, 380k, 420k, 460k at 8%.

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Example 10 — Geometric gradient: first payment PHP 400,000, growth 5%, 6 payments, discount 10%.

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Example 11 — Geometric special case: A1 = PHP 250,000, i = g = 6%, n = 8.

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Example 12 — Civil application: maintenance begins at PHP 1.2M in year 1 and rises PHP 150k/year for 7 years at 9%.

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Example 13 — A perpetual annual maintenance cost of PHP 300,000 begins one year from now. Find its present worth at 6% per year.

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