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Deferred Annuities

A deferred annuity begins after a delay. First compute the value at the start of the annuity, then discount or compound to the required date.

Problem: CE Board May 2015

In 5 years, P1.8 M is needed for renovation. A sinking fund of three annual payments is established now, with no payments after 3 years. Find the payment if money is worth 15%.

$$F_1=A(F/A,15\%,3)=3.4725A$$
$$1,800,000=3.4725A(1.15)^2$$

Final answer: $A=P391,600$.

Problem: CE Board May 2004

A boy receives 10 yearly endowments of P30,000 each starting at the end of the 11th year. At 8%, what is the value now?

$$P_1=30000(P/A,8\%,10)=201,302.44$$
$$P=\frac{201,302.44}{(1.08)^{10}}=93,241.98$$

Final answer: P93,241.98.

Problem: Deferred Annuity Present Worth

Find the present worth of P8,000 paid annually for 5 years, first payment at the end of year 4, if i = 10%.

$$P_3=8000(P/A,10\%,5)=8000(3.7908)=30326$$
$$P_0=30326(P/F,10\%,3)=30326(0.7513)=22789$$

Answer: The present worth is about P22,789.

Problem: Deferred Maintenance Fund

A maintenance fund pays P12,000 each year from year 6 through year 10. At 9%, find the present worth.

$$P_5=12000(P/A,9\%,5)=12000(3.8897)=46676$$
$$P_0=46676(P/F,9\%,5)=46676(0.6499)=30335$$

Answer: The present worth is about P30,335.

Problem: Future Worth of a Deferred Series

Deposits of P5,000 are made at the end of years 3 to 8. Find the amount at year 8 for i = 6%.

$$F_8=5000(F/A,6\%,6)=5000(6.9753)=34877$$

Answer: The future worth at year 8 is about P34,877.

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Exam Generator Problems

Additional board-style practice items for this topic.

Question Bank: q186

MSTE - Engineering Economy / Uniform Gradient Series / Engr. Janclyde Espinosa (Clidez)

The maintenance of Isuzu diesel engine is expected to be 155 dollars at the end of the first year and it is expected to increase by 35 dollars each year for the following years. What sum of money should be set aside now to pay the maintenance for the eight-year period? Assume MARR to be 6%.
Present worth factor (P/A, 6%, 8) = 6.2098
Sinking fund factor (A/F, 6%, 8) = 0.1010
Compound amount factor (F/A, 6%, 8) = 9.897
Uniform gradient series factor (P/G, 6%, 8) = 19.845

Answer:

  1. 1657
  2. 1756
  3. 1567
  4. 1675
For an arithmetic gradient, the present worth is the first annual amount plus the gradient amount:
$P = A_1(P/A,6\%,8)+G(P/G,6\%,8)$
$P = 155(6.2098)+35(19.845)$
$P = 962.52+694.58 = 1{,}657.10$
$\boxed{P \approx 1657}$

Question Bank: t1031

MSTE - Engineering Economy / Engineering Economy / Gemini mapped Chapter 7 to 10

The present value of an annuity of "R" pesos payable annually for 8 years, with the first payment at the end of 10 years, is P187,481.25. Find the value of R if money is worth 5%.

  1. P45,000
  2. P44,000
  3. P42,000
  4. P43,000

Solution pending in psadquestions/t1031.json.