Question
To pay off a debt we must repay a capital of 5000 euros today, a capital of 5000 euros in 3 years and a capital of 5000 euros in 9 years. We agree to pay off the debt in a single installment in 6 years; How much will we have to pay if the annual compound rate is 4.25%?
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Answer to a math question To pay off a debt we must repay a capital of 5000 euros today, a capital of 5000 euros in 3 years and a capital of 5000 euros in 9 years. We agree to pay off the debt in a single installment in 6 years; How much will we have to pay if the annual compound rate is 4.25%?
Nash
4.987 Answers
To find out how much we need to pay after 6 years with an annual compound rate of 4.25%, we need to calculate the future value of each payment and then add them up.
Step 1: Calculate the future value of β¬5000 paid in 6 years:
Future Value = Present Value * (1 + Rate)^N
Future Value = β¬5000 * (1 + 0.0425)^6
Step 2: Calculate the future value of β¬5000 paid in 3 years:
Future Value = β¬5000 * (1 + 0.0425)^3
Step 3: Calculate the future value of β¬5000 paid in 9 years:
Future Value = β¬5000 * (1 + 0.0425)^9
Step 4: Add up all future values to find the total amount to be paid:
Total = Future Value1 + Future Value2 + Future Value3
Now, let's calculate the total amount to be paid:
1.Future Value_1 = β¬5000 * (1 + 0.0425)^6
Future Value_1 = β¬5000 * (1.0425)^6 β β¬5000 * 1.2882 = β¬6441
2.Future Value_2 = β¬5000 * (1 + 0.0425)^3
Future Value_2 = β¬5000 * (1.0425)^3 β β¬5000 * 1.1301 = β¬5650.50
3.Future Value_3 = β¬5000 * (1 + 0.0425)^9
Future Value_3 = β¬5000 * (1.0425)^9 β β¬5000 * 1.4350 = β¬7175
4.Total = Future Value_1 + Future Value_2 + Future Value_3
Total β β¬6441 + β¬5650.50 + β¬7175 = β¬19266.50
Therefore, you will need to pay approximately β¬19266.50 after 6 years with an annual compound rate of 4.25%.
\boxed{Answer: β¬19266.50}
Step 1: Calculate the future value of β¬5000 paid in 6 years:
Future Value = Present Value * (1 + Rate)^N
Future Value = β¬5000 * (1 + 0.0425)^6
Step 2: Calculate the future value of β¬5000 paid in 3 years:
Future Value = β¬5000 * (1 + 0.0425)^3
Step 3: Calculate the future value of β¬5000 paid in 9 years:
Future Value = β¬5000 * (1 + 0.0425)^9
Step 4: Add up all future values to find the total amount to be paid:
Total = Future Value1 + Future Value2 + Future Value3
Now, let's calculate the total amount to be paid:
1.
2.
3.
4.
Therefore, you will need to pay approximately β¬19266.50 after 6 years with an annual compound rate of 4.25%.
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