We will use the loan payment formula to solve this problem, which is based on the annuity formula:

$P = \dfrac{A \cdot r}{1 - (1 + r)^{-nt}}$

Where:

• $P$ is the regular payment.
• $A$ is the loan amount ($110,000).
• $r$ is the interest rate per period.
• $n$ is the number of payments per year (1 for yearly, 12 for monthly, 26 for biweekly, 52 for weekly).
• $t$ is the term of the loan in years (20 years).
• $APR$ is the annual interest rate (4% or 0.04).

Part a: Finding Regular Payments

We need to compute the payments for $n = 1$, $n = 12$, $n = 26$, and $n = 52$. First, let's calculate the interest rate per period ($r$) for each scenario:

$r_{\text{yearly}} = \dfrac{0.04}{1} = 0.04$ $r_{\text{monthly}} = \dfrac{0.04}{12} = 0.0033333$ $r_{\text{biweekly}} = \dfrac{0.04}{26} = 0.00153846$ $r_{\text{weekly}} = \dfrac{0.04}{52} = 0.00076923$

Now we can use the loan payment formula for each case.

I'll compute the payments for each case step-by-step.

Part b: Total Payments

Once the periodic payments are calculated, we can find the total payment by multiplying the regular payment by the total number of payments over the loan's lifetime, which is $n \times t$.

Let's calculate each case next.### Part a: Regular Payments

• Yearly payments ($n = 1$): $8,094
• Monthly payments ($n = 12$): $667
• Biweekly payments ($n = 26$): $307
• Weekly payments ($n = 52$): $154

Part b: Total Payments

• For $n = 1$ (yearly), total amount paid: $161,880
• For $n = 12$ (monthly), total amount paid: $159,979
• For $n = 26$ (biweekly), total amount paid: $159,885
• For $n = 52$ (weekly), total amount paid: $159,845

Part c: Comparison of Total Payments

The total amount paid decreases slightly as the payment frequency increases, with weekly payments resulting in the lowest total amount paid.

Do you need further details or have any questions?

---

Here are five related questions for practice:

1. How would the payments change if the interest rate was higher, say 5%?
2. What would the payments be if the loan term was reduced to 15 years?
3. How does the frequency of payments affect the total interest paid over time?
4. If you wanted to borrow a higher amount, say $150,000, how would the payments change?
5. How would the payments differ if you opted for biweekly payments but a 30-year loan term?

Tip: Making more frequent payments typically reduces the total interest paid over the life of the loan.