February 2017

Perform the indicated operation and express the answer in the form of $a + bi$: $(5 + 4i) + 2(2 - 3i) - i(1 - 5i)$

Find the present value of installment payments of P1,000 now, P2,000 at the end of the first year, P3,000 at the end of the second year, P4,000 at the end of the third year, P5,000 at the end of the fourth year, if money is worth 10% compounded annually.

The first cost of a certain machine is P90,000. After 8 years it will have a salvage value of P18,000. Compute the book value at the end of 3 years by using the sum of the years digit method.

The annual income from the mine is P100,000 and the life of the mine is 20 years. Find the price that an investor is willing to pay for the mine if he considers that money is worth 5% and if he is to accumulate a sinking fund at 6% in order to replace the capital he invested.

At what nominal rate compounded quarterly will payments of P800 quarterly for 5 years discharge all liabilities of a debtor who borrows P14,000 today?

A concrete mixer was bought for P30,000 six years ago. It will have a salvage value of P3,000 four years from now. It is sold now at P8,000. What is the sunk cost if the depreciation used is sinking fund method at 6%? Hint: sunk cost is the difference between the book value and the selling price.

A solid shaft made from copper is 90mm diameter and 8m long. If this shaft is joined to a 1.5m long solid steel shaft and 120mm diameter, estimate the maximum shear stress in each material and the total angle of twist of the entire shaft, if a torque of 20KN-m is applied to each end of shaft. GC=40GN/m2 G=90GN/m2