This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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Question 4: a) Calculate the simple interest on N5000 at 8% per annum for 3 years. Step 1: Identify the principal (P), rate (R), and time (T). P = N\5000 R = 8\% = 0.08 T = 3 years Step 2: Use the simple interest formula I = PRT. I = 5000 × 0.08 × 3 I = 400 × 3 I = N\1200 The simple interest is N\1200. b) Find the compound amount if N4000 is invested at 6% per annum compounded annually for 4 years. Step 1: Identify the principal (P), rate (R), and time (T). P = N\4000 R = 6\% = 0.06 T = 4 years Step 2: Use the compound interest formula A = P(1+R)^T for annual compounding. A = 4000(1+0.06)^4 A = 4000(1.06)^4 A = 4000 × 1.26247696 A = N\5049.91 The compound amount is N\5049.91. c) Compare simple and compound interest for N3000 at 5% over 2 years. Step 1: Calculate the simple interest. P = N\3000 R = 5\% = 0.05 T = 2 years I_simple = PRT = 3000 × 0.05 × 2 I_simple = 150 × 2 = N\300 Step 2: Calculate the compound interest. First, find the compound amount: A = P(1+R)^T = 3000(1+0.05)^2 A = 3000(1.05)^2 A = 3000 × 1.1025 A = N\3307.50 Then, find the compound interest: I_compound = A - P = 3307.50 - 3000 = N\307.50 Step 3: Compare the two interests. The simple interest is N300. The compound interest is N307.50. The compound interest is N\7.50 higher than the simple interest. Question 5: a) Convert N10000 to US Dollars if 1 USD = 18.50 NAD. Step 1: Use the given exchange rate to convert NAD to USD. Amount in USD = Amount in NADExchange rate (NAD per USD) Amount in USD = (10000)/(18.50) Amount in USD ≈ USD 540.54 N10000 is approximately USD 540.54. b) A student exchanges USD 500 to Namibian Dollars. How much do they receive? Step 1: Use the given exchange rate to convert USD to NAD. Amount in NAD = Amount in USD × Exchange rate (NAD per USD) Amount in NAD = 500 × 18.50 Amount in NAD = N\9250 They receive N\9250. c) Explain two factors that influence exchange rates. • Interest Rates: Higher interest rates in a country can attract foreign investment, increasing demand for that country's currency and causing its exchange rate to appreciate. • Inflation: A country with consistently lower inflation rates than another will see its currency's value appreciate relative to the other currency, as its purchasing power is maintained better. Question 6: A business invests N8000 at 7% compound interest for 3 years and then converts the final amount to USD at an exchange rate of 1 USD = 19 NAD. a) Calculate the final amount in NAD. Step 1: Identify the principal (P), rate (R), and time (T). P = N\8000 R = 7\% = 0.07 T = 3 years Step 2: Use the compound interest formula A = P(1+R)^T. A = 8000(1+0.07)^3 A = 8000(1.07)^3 A = 8000 × 1.225043 A = N\9800.344 The final amount in NAD is N\9800.34. b) Convert the final amount to USD. Step 1: Use the final amount from part a) and the given exchange rate. Final amount in NAD = N9800.344 Exchange rate: 1 USD = 19 NAD Amount in USD = Final amount in NADExchange rate (NAD per USD) Amount in USD = (9800.344)/(19) Amount in USD ≈ USD 515.81 The final amount converted to USD is USD 515.81. That's 2 down. 3 left today — send the next one.