Let's break down the calculation: **Loan Amount (Principal):** $10,000 **Annual Interest Rate:** 10% **Term:** 5 years ### If Paid as a Simple Interest Loan Simple interest formula: \[ \text{Total Interest} = P \times r \times t \] where - \( P = \$10,000 \) - \( r = 10\% = 0.10 \) - \( t = 5 \) years \[ \text{Total Interest} = \$10,000 \times 0.10 \times 5 = \$5,000 \] \[ \text{Total Payment} = \text{Principal} + \text{Interest} = \$10,000 + \$5,000 = \$15,000 \] --- ### If Paid as an Amortized (Installment) Loan For most personal loans, payments are made monthly and the total paid is a bit less than simple interest because the principal reduces over time. The monthly payment formula for an amortizing loan: \[ M = P \frac{r(1+r)^n}{(1+r)^n - 1} \] where - \( P = \$10,000 \) - \( r = \text{monthly interest rate} = 10\% / 12 = 0.008333 \) - \( n = \text{number of payments} = 5 \times 12 = 60 \) Plug in the numbers: \[ M = 10000 \times \frac{0.008333(1+0.008333)^{60}}{(1+0.008333)^{60} - 1} \] Calculate \((1+0.008333)^{60}\): First, \(1+0.008333 = 1.008333\) \[ 1.008333^{60} \approx 1.647 \] So, \[ M = 10000 \times \frac{0.008333 \times 1.647}{1.647 - 1} = 10000 \times \frac{0.01373}{0.647} \approx 10000 \times 0.02122 \approx \$212.20 \] So the **monthly payment** is about **\$212.20**. Total paid over 60 months: \[ \$212.20 \times 60 = \$12,732 \] --- ## **Summary** - **Simple Interest:** **\$15,000** total paid - **Typical Amortized Loan:** **\$12,732** total paid If you meant a standard loan with monthly payments, the total cost to pay back the loan is **about \$12,732**. If you meant just simple interest, it would be **\$15,000**. **Let me know if you want a breakdown for a different payment schedule!**