CE Board Exam Randomizer

⬅ Back to Engineering Economy Topics

Annuities and Present Worth

An annuity is a uniform series of equal payments made at equal time intervals.

$$P=A\left(\frac{1-(1+i)^{-n}}{i}\right)$$

Present Worth of Annual Savings

Find the present worth of Php 15,000 received every year for 5 years at 8% interest.

$$P=15000\left(\frac{1-(1.08)^{-5}}{0.08}\right)$$
$$P=15000(3.9927)=59,890.50$$

Final answer: Php 59,890.50.

Problem: Present Worth of Uniform Savings

Annual savings of P25,000 occur for 6 years. Find present worth at 9%.

$$P=25000(P/A,9\%,6)=25000(4.4859)=112148$$

Answer: Present worth is about P112,148.

Problem: Future Worth of Uniform Deposits

P12,000 is deposited at the end of each year for 5 years at 8%. Find future worth.

$$F=12000(F/A,8\%,5)=12000(5.8666)=70399$$

Answer: Future worth is about P70,399.

Problem: Required Annual Payment

Find the annual payment needed to recover P200,000 over 5 years at 10%.

$$A=200000(A/P,10\%,5)=200000(0.26380)=52760$$

Answer: The annual payment is about P52,760.

Problem: Present Worth with Uniform Receipts and Salvage

A project receives P40,000 per year for 4 years plus P30,000 salvage at year 4. Use i = 10%.

$$P=40000(P/A,10\%,4)+30000(P/F,10\%,4)$$
$$P=40000(3.1699)+30000(0.6830)=147286$$

Answer: Present worth is about P147,286.

Scroll to zoom