1. **State the problem:** We want to calculate the total interest paid on a loan of $169255 with an annual interest rate of 4%, paid monthly over 30 years. 2. **Identify variables:** - Principal ($P$) = 169255 - Annual interest rate ($r$) = 4% = 0.04 - Number of years ($t$) = 30 - Number of payments per year ($n$) = 12 3. **Calculate monthly interest rate:** $$ i = \frac{r}{n} = \frac{0.04}{12} = 0.0033333333 $$ 4. **Calculate total number of payments:** $$ N = n \times t = 12 \times 30 = 360 $$ 5. **Calculate monthly payment using the formula for an amortizing loan:** $$ M = P \times \frac{i (1+i)^N}{(1+i)^N -1} $$ Substituting values: $$ M = 169255 \times \frac{0.0033333 (1+0.0033333)^{360}}{(1+0.0033333)^{360} -1} $$ 6. **Compute $(1+i)^{360}$:** $$ (1.0033333)^{360} \approx 3.2434 $$ 7. **Calculate numerator:** $$ 0.0033333 \times 3.2434 = 0.0108113 $$ 8. **Calculate denominator:** $$ 3.2434 -1 = 2.2434 $$ 9. **Calculate monthly payment:** $$ M = 169255 \times \frac{0.0108113}{2.2434} = 169255 \times 0.004817 = 815.18 $$ 10. **Calculate total amount paid over 30 years:** $$ \text{Total paid} = M \times N = 815.18 \times 360 = 293464.80 $$ 11. **Calculate total interest paid:** $$ \text{Interest} = \text{Total paid} - P = 293464.80 - 169255 = 124209.80 $$ 12. **Round to nearest hundredth:** Interest is already to two decimal places. **Final answer:** The total interest paid is $124209.80$.