Question

Phoenix Pump and Filter projects that the cost of steel bodies for Model R910 valves will increase by $2.50 every 3 months. If the cost for the first quarter is expected to be $90 per unit, what is the present worth of a unit's costs over a 3- year time period at an interest rate of 12% per year compounded quarterly?

Answer 1

Answer:

$1023.98

Explanation:

Using the standard notation equation for annual payment and for arithmetic gradient to calculate the present worth of a unit's costs; we have the following corresponding expression.

P = A (P/A, i, n)         &     P = G (P/G, i, n)

where;

A = annual payment

G = arithmetic gradient

n = number of years

i = annual interest rate

From the question;

the payment  period = compounding period

∴ quaterly interest rate = 3%

The present worth value of the unit's cost is therefore shown as

P = 90 (P/A, 3%, 12) + 2.5(P/G, 3%, 12)

P = 90(9.954) + 2.5(51.2481)

P = $1023.98

∴ The present worth value of the unit's cost = $1023.98