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Define equivalent worth and ROR; deposit to draw monthly

Short answer

Equivalent worth is the value at a single date of cash flows moved at the MARR. Rate of return is the interest rate that makes PW of net cash flow zero, accepted if ≥ MARR. Deposit needed: Rs 824,215 (8% per year compounded monthly, 120 withdrawals of Rs 10,000).

Define equivalent worth and rate of return method. How much rupees should you deposit now in a bank account that gives 8% interest per year if you wish to draw Rs. 10,000 per month for 10 years?

Equivalent worth

Equivalent worth is the value, at one chosen date, of a whole set of cash flows when each flow is moved to that date using the interest rate (MARR). Cash flows at different times become comparable only after this move. Three forms are used: present worth (PW) at time 0, future worth (FW) at the end of the project, and annual worth (AW) as a uniform yearly amount.

Rate of return (ROR) method

The ROR (internal rate of return) is the interest rate i* at which the PW (or AW, FW) of the net cash flow is zero, i.e. PW of inflows = PW of outflows. The project is accepted if i* ≥ MARR. It is found by trial and error with interpolation.

Numerical: deposit needed

Assumption: 8% per year is the nominal rate, compounded monthly. Withdrawals are at the end of each month, so this is an annuity.

 P = ?
 |
 0   1   2   3  ...  119  120   (months)
     ↑   ↑   ↑        ↑    ↑
   10,000 each month (A)
  • Monthly interest i = 8% / 12 = 0.6667% = 0.006667
  • Number of months n = 10 × 12 = 120
  • P = A (P/A, i, n)
  • (P/A, 0.6667%, 120) = [1 − (1.006667)^-120] / 0.006667 = 82.4215
  • P = 10,000 × 82.4215 = Rs 824,214.81

Answer: Rs 824,215 should be deposited now (about Rs 8.24 lakh).

If 8% is taken as the effective annual rate, monthly i = (1.08)^(1/12) − 1 = 0.6434% and P = Rs 834,324.

✓ Answer checked by Claude Opus 5.5 (high effort)

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