Interest Calculations
1. Problem: Rhemia invested 3000 at 3.9% annually for 5 years. Find the amount after 5 years.
Step 1: Use the simple interest formula $$A = P(1 + rt)$$ where $P=3000$, $r=0.039$, $t=5$.
Step 2: Calculate $$A = 3000(1 + 0.039 \times 5) = 3000(1 + 0.195) = 3000 \times 1.195 = 3585$$.
Step 3: The amount after 5 years is 3585.
2. Problem: Joshua’s sales commission rate is 6%. Find commission from sales of 120500.
Step 1: Commission = rate × sales = 0.06 × 120500.
Step 2: Calculate $$0.06 \times 120500 = 7230$$.
Step 3: Joshua’s commission is 7230.
3. Problem: Sales tax on an item costing 250 at 6%. Find tax and total price.
Step 1: Sales tax = cost × rate = 250 × 0.06.
Step 2: Calculate $$250 \times 0.06 = 15$$.
Step 3: Total price = cost + tax = 250 + 15 = 265.
Step 4: Sales tax is 15 and total price is 265.
4. Problem: Vangie loaned 30000 with interest 5700 for 2 years. Find interest rate.
Step 1: Use simple interest formula $$I = Prt$$, solve for $r$: $$r = \frac{I}{Pt}$$.
Step 2: Calculate $$r = \frac{5700}{30000 \times 2} = \frac{5700}{60000} = 0.095 = 9.5\%$$.
Step 3: Interest rate is 9.5%.
5. Problem: Joemar deposits 3000 for 2 years at 8% per annum. Find interest after 1 and 2 years.
Step 1: Interest for 1 year: $$I_1 = P \times r \times 1 = 3000 \times 0.08 \times 1 = 240$$.
Step 2: Interest for 2 years: $$I_2 = 3000 \times 0.08 \times 2 = 480$$.
Step 3: Interest after one year is 240, after two years is 480.