1. **Problem statement:** Neeraj took a loan of 400000 for 2 years at 10% annual compound interest. He paid 240000 at the end of the first year. 2. **Formula for compound interest:** $$CI = P \left(1 + \frac{R}{100}\right)^T - P$$ Where $P$ is the principal, $R$ is the annual interest rate, $T$ is the time in years, and $CI$ is the compound interest. 3. **First year compound interest calculation:** Principal $P = 400000$, Rate $R = 10\%$, Time $T = 1$ year. Calculate amount after 1 year: $$A = 400000 \times \left(1 + \frac{10}{100}\right)^1 = 400000 \times 1.1 = 440000$$ Compound interest for first year: $$CI = A - P = 440000 - 400000 = 40000$$ 4. **Total interest paid in two years:** At the end of first year, Neeraj paid 240000, so remaining principal for second year: $$P_2 = 440000 - 240000 = 200000$$ Amount after second year: $$A_2 = 200000 \times 1.1 = 220000$$ Compound interest for second year: $$CI_2 = 220000 - 200000 = 20000$$ Total interest paid in two years: $$CI_{total} = 40000 + 20000 = 60000$$ --- 1. **Problem statement:** Neelam bought a machine for 40000. The price depreciates at 5% annually. After some years, it was sold for 36100. 2. **Depreciation formula:** $$A = P \times (1 - r)^t$$ Where $A$ is the amount after $t$ years, $P$ is initial price, $r$ is depreciation rate, $t$ is time in years. 3. **Depreciation in first year:** $$Depreciation = P \times r = 40000 \times 0.05 = 2000$$ 4. **Find number of years $t$:** $$36100 = 40000 \times (1 - 0.05)^t = 40000 \times 0.95^t$$ Divide both sides by 40000: $$0.9025 = 0.95^t$$ Take natural log: $$\ln(0.9025) = t \ln(0.95)$$ $$t = \frac{\ln(0.9025)}{\ln(0.95)} \approx \frac{-0.1025}{-0.0513} \approx 2$$ 5. **Profit or loss percentage if rent income is 4900:** Total money received = selling price + rent = 36100 + 4900 = 41000 Profit = 41000 - 40000 = 1000 Profit percentage: $$\frac{1000}{40000} \times 100 = 2.5\%$$ --- 1. **Problem statement:** Ramesh had 207345 Nepali rupees. Exchange rates: buying rate 138.23, selling rate 138.83. 2. **Exchange rate used when exchanging Nepali rupees to USD:** Selling rate is used when converting Nepali rupees to USD. 3. **USD obtained from 207345 Nepali rupees:** $$USD = \frac{207345}{138.83} \approx 1493.07$$ 4. **Percent devaluation when selling rate is 140.2183:** Original selling rate = 138.83 New selling rate = 140.2183 Percent devaluation: $$\frac{140.2183 - 138.83}{138.83} \times 100 \approx \frac{1.3883}{138.83} \times 100 \approx 1.0\%$$