- 2066 Magh · 6 marks
Deposit for infinite bimonthly withdrawals
Short answer
With 12% nominal annual rate, the two-monthly interest rate is 2%. Capitalized worth = 5000/0.02 = Rs 2,50,000.
How much money should Mr Ram deposit now in a bank so that he and his successor can draw Rs 5000 bimonthly for infinite period? Interest rate is 12% per year.
Assumption: "bimonthly" means once every two months, so there are 6 withdrawals per year. 12% per year is the nominal rate compounded every two months.
P = ? withdrawals of 5,000 at months 2, 4, 6, 8, ... forever
- Interest per two-month period i = 12% / 6 = 2% = 0.02
- Withdrawal per period A = Rs 5,000
- For an infinite series, P = A / i (capitalized worth)
- P = 5,000 / 0.02 = Rs 2,50,000
The deposit is never used up because each period's interest (2% of 2,50,000 = Rs 5,000) is exactly the amount drawn, so the principal stays intact for the successors.
Answer: Rs 2,50,000 should be deposited now.
(If the withdrawal were twice a month, i = 0.5% per half-month and P = 5,000/0.005 = Rs 10,00,000.)
✓ Answer checked by Claude Opus 5.5 (high effort)
Related questions
- Capitalized worth; deposit for perpetual withdrawals · Engineering Economics, chapter 2
- Capitalized worth and infinite-period deposit · Engineering Economics, chapter 2
- Deposit now to draw growing monthly amount · Engineering Economics, chapter 2
- Car loan interest rate and lump sum at year 3 · Engineering Economics, chapter 2
- Define equivalent worth and ROR; deposit to draw monthly · Engineering Economics, chapter 2
- Nominal vs effective rate; simple vs compound deposit · Engineering Economics, chapter 2
- Rate analysis: 12.5 mm plaster 1:5, per m² · Estimating and Costing, chapter 4 · asked 3×
- Rate analysis: 12.5 mm plaster 1:3, per 100 m² · Estimating and Costing, chapter 4
- Guide bank and launching apron, 5000 m3/s · Irrigation and Drainage Engineering, chapter 6
- EPS and book value; 5000 shares, EBIT 3,50,000 · Project Engineering, chapter 6 · asked 2×