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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 33: 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 35: 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.

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