Common Patterns Question 2

An asset pays $30 in month one and increases by $30 per month until month 20, when you begin to receive $600 per month through month 35. Your monthly discount rate is 2%.

- What is the factor notation for months 1 - 20?

This is an irregular series that can be separated into a linear gradient from periods 0 to 20 and a constant series in period 21-35.

$30(P|G, i=2\%, 21) (1+.02)$
Multiplying by (1+.02) will shift it to period 1

- What is the factor notation for the benefits in months 21-35?

Switches to a constant series.

$\frac{600(P|A, i=2\%, 15)}{(1+.02)^{20}}$
dividing by $(1+.02)^{20}$ shifts it to period 21

- What is the present value of this asset?

For periods 1 - 20: (30)(157.7959)(1.02) = $4828.55

For periods 21 - 35: $\frac{600(12.8493)}{1.02^{20}}$ = $5,188.32

$4828.55 + $5,188.32 = $10,016.90

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