A series of 12 annual payments of 2000 is equivalent to thre

A series of 12 annual payments of $2000 is equivalent to three equal payments, one each at the end of 12 years, 15 years, and 20 years. The interest rate is lo%, compound annually. What is the amount of the three equal payments? Ans. $19 284.55

Solution

Present value (PV) of the 12 annual payments = $2,000 x PVIFA (10%, 12 years) = $2,000 x 6.8137 [From PVIFA Table]

= $13,627.4

If the annual payment required be Z, then

$13,627.4 = Z / (1.1)¹² + Z / (1.1)¹⁵ + Z / (1.1)²⁰

$13,627.4 = Z x (0.3186 + 0.2394 + 0.1486)

$13,627.4 = Z x 0.7066

Z = $13,627.4 / 0.7066 = $19,284.69**

** The slight difference is due to rounding-off effects.