Key Concept: Advanced Scenario Analysis, Complex Calculation
b) 1,125
[Solution Description] To solve this problem, we first need to calculate the interest for each partner separately considering any changes in their capital contributions during the year.
For Partner A:
The principal is 10,000, the rate is 5%, and the time is 1 year. Using the formula for interest:
$$I_A = P \times R \times T = 10000 \times 0.05 \times 1 = 500$$
So, the interest earned by Partner A is 500.
For Partner B:
Initially, the principal was 15,000, but it changed to 10,000 after half a year. We need to calculate the interest for the two different periods.
Interest for the first half-year:
$$I_{B_1} = 15000 \times 0.05 \times \frac{1}{2} = 375$$
After withdrawing \$5,000, the new principal becomes \$10,000 for the remaining half of the year:
$$I_{B_2} = 10000 \times 0.05 \times \frac{1}{2} = 250$$
Total interest for Partner B:
$$I_B = I_{B_1} + I_{B_2} = 375 + 250 = 625$$
Therefore, the total interest for both partners is:
$$I_{\text{Total}} = I_A + I_B = 500 + 625 = 1125$$
Hence, the total interest on capital for both partners by the end of the year is 1,125.
Your Answer is correct.
b) 1,125
[Solution Description] To solve this problem, we first need to calculate the interest for each partner separately considering any changes in their capital contributions during the year.
For Partner A:
The principal is 10,000, the rate is 5%, and the time is 1 year. Using the formula for interest:
$$I_A = P \times R \times T = 10000 \times 0.05 \times 1 = 500$$
So, the interest earned by Partner A is 500.
For Partner B:
Initially, the principal was 15,000, but it changed to 10,000 after half a year. We need to calculate the interest for the two different periods.
Interest for the first half-year:
$$I_{B_1} = 15000 \times 0.05 \times \frac{1}{2} = 375$$
After withdrawing \$5,000, the new principal becomes \$10,000 for the remaining half of the year:
$$I_{B_2} = 10000 \times 0.05 \times \frac{1}{2} = 250$$
Total interest for Partner B:
$$I_B = I_{B_1} + I_{B_2} = 375 + 250 = 625$$
Therefore, the total interest for both partners is:
$$I_{\text{Total}} = I_A + I_B = 500 + 625 = 1125$$
Hence, the total interest on capital for both partners by the end of the year is 1,125.