1. **State the problem:** You borrow 5000 and agree to repay in 36 equal monthly payments with a monthly interest rate of 1% (12% annual compounded monthly). Find the monthly payment (pmt). 2. **Given:** - Present value, $PV = 5000$ - Annual interest rate, $r = 12\% = 0.12$ - Number of years, $n = 3$ - Number of months per year, $m = 12$ - Number of payments, $N = n \times m = 36$ - Monthly interest rate, $i = \frac{r}{m} = \frac{0.12}{12} = 0.01$ 3. **The amortization formula (ordinary annuity present value formula) is:** $$ PV = pmt \times \frac{1 - (1 + i)^{-N}}{i} $$ 4. **Plug in the known values:** $$ 5000 = pmt \times \frac{1 - (1 + 0.01)^{-36}}{0.01} $$ 5. **Calculate the bracket term:** First compute $(1 + 0.01)^{-36}$: $$ (1.01)^{-36} = \frac{1}{(1.01)^{36}} $$ Using a calculator, $(1.01)^{36} \approx 1.430768783$ Thus, $$ (1.01)^{-36} = \frac{1}{1.430768783} \approx 0.699676$ 6. **Compute the numerator:** $$ 1 - 0.699676 = 0.300324 $$ 7. **Compute the entire fraction:** $$ \frac{0.300324}{0.01} = 30.0324 $$ 8. **Solve for $pmt$:** $$ 5000 = pmt \times 30.0324 \implies pmt = \frac{5000}{30.0324} \approx 166.53 $$ **Final answer:** The monthly payment should be approximately **166.53** to pay off the loan in 36 months including interest.