Capitalized worth and infinite-period deposit

Capitalized worth

Capitalized worth (CW) is the present worth of a series of cash flows that continues forever (infinite life). For a uniform end-of-period amount A at interest rate i per period: CW = P = A / i It is the sum which, when deposited, earns interest enough to pay A every period without reducing the principal. It is used for permanent structures such as dams, bridges and endowments.

Interest rates

Monthly i = 0.75%.

• Yearly effective rate: i_y = (1.0075)¹² − 1 = 9.3807%
• Four-yearly effective rate: i_4 = (1.0075)⁴⁸ − 1 = 43.1405%

(i) Rs 6,000 monthly

P₁ = 6,000 / 0.0075 = Rs 800,000

(ii) Rs 100,000 yearly

P₂ = 100,000 / 0.093807 = Rs 1,066,020

(iii) Rs 500,000 every four years

P₃ = 500,000 / 0.431405 = Rs 1,159,003

Total deposit

P = 800,000 + 1,066,020 + 1,159,003 = Rs 3,025,023

Answer: Rs 800,000 for (i), Rs 1,066,020 for (ii), Rs 1,159,003 for (iii); total about Rs 30.25 lakh. (First withdrawal of each series is taken at the end of the first period.)