A loan of $15,000 is to be repaid in 5 equal annual installments with an interest rate of 6% per annum. What is the amount of each installment?
["How to Repay a $15,000 Loan in 5 Equal Annual Installments with 6% Interest – Find Your Monthly Payment", "Taking out a $15,000 loan and repaying it in structured annual payments can feel overwhelming — but with the right calculation method, you can easily determine the exact amount of each installment. This article breaks down how to calculate the yearly repayment amount for a $15,000 loan repaid over 5 equal annual installments at a 6% annual interest rate.", "---", "### Understanding Installment Loan Calculation", "A loan repaid in fixed annual installments involves amortization, where each payment includes both interest and principal repayment. With equal annual payments and a fixed 6% interest rate, the formula to calculate the annual installment is based on the present value of an ordinary annuity.", "The formula for the annual installment P is:", "[\nP = \frac{L \ imes r}{1 - (1 + r)^{-n}}\n]", "Where:\n- ( L = 15,000 ) = loan principal\n- ( r = 0.06 ) = annual interest rate (6%)\n- ( n = 5 ) = number of annual payments", "---", "### Step-by-Step Calculation", "1. Plug values into the formula:", "[\nP = \frac{15,000 \ imes 0.06}{1 - (1 + 0.06)^{-5}}\n]", "2. Calculate the denominator:", "[\n(1 + 0.06)^{-5} = 1.06^{-5} \approx 0.7473\n]", "[\n1 - 0.7473 = 0.2527\n]", "3. Compute the numerator:", "[\n15,000 \ imes 0.06 = 900\n]", "4. Divide to get the installment:", "[\nP = \frac{900}{0.2527} \approx 3,558.71\n]", "---", "### Final Result", "Each annual installment to repay a $15,000 loan over 5 years at 6% interest is approximately $3,558.71.", "---", "### Why This Calculation Matters", "Using an exact formula ensures accurate payments without overpaying interest. This approach is common for personal loans, bonds, and mortgage planning. It helps borrowers budget accurately and avoid payment errors.", "---", "### Summary", "- Loan amount: $15,000\n- Term: 5 years\n- Interest rate: 6% per year\n- Equal annual installments: $3,558.71", "By understanding this calculation, you gain clarity on how fixed installments reduce both principal and interest evenly each year — giving you full control over your repayment plan.", "---", "Keywords: annual installment loan, $15,000 loan repayment, amortization formula, $15,000 installment payment 6%, how to calculate loan installments"]
