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Let's work through the problem step by step.

### **Part (a): Total in Mr. Hughes' RRSP Account**

Mr. Hughes contributed **$4,000 per year for 10 years** at an interest rate of **9% compounded annually**. After the 10 years, the accumulated amount stays for another 5 years at the same interest rate.

To solve this, we need to find the future value of an annuity first, and then calculate the amount after 5 years of compound interest on that accumulated sum.

#### Step 1: Future Value of an Annuity
The formula for the future value of an annuity compounded annually is:

\[
FV = P \times \left( \frac{(1 + r)^n - 1}{r} \right)
\]

Where:
- $P = 4,000$ is the annual contribution.
- $r = 0.09$ (9% annual interest rate).
- $n = 10$ is the number of years.

#### Step 2: Let the amount accumulate for another 5 years
The future value after 10 years is then compounded for another 5 years at the same rate. The formula for compound interest is:

\[
A = P \times (1 + r)^n
\]

Where:
- $P$ is the accumulated value after 10 years (from step 1).
- $r = 0.09$.
- $n = 5$.

---

### **Part (b): Total Contribution**
The total amount contributed by Mr. Hughes is simply:

\[
\text{Total Contribution} = \text{Annual Contribution} \times \text{Number of Years}
\]

\[
= 4,000 \times 10 = 40,000
\]

---

### **Part (c): Interest Earned**
The interest earned is the difference between the total amount in the account after 15 years (from part a) and the total contribution (from part b):

\[
\text{Interest Earned} = \text{Total Amount} - \text{Total Contribution}
\]

---

### **Part (6): Loan Interest**
For the loan part, we are asked to calculate the total interest paid on a loan with ordinary monthly payments of $715, over 7 years, at 9.12% compounded monthly.

For this, we use the formula for the **future value of an annuity** with monthly compounding:

\[
FV = P \times \left( \frac{(1 + \frac{r}{12})^{12n} - 1}{\frac{r}{12}} \right)
\]

Where:
- $P = 715$ (monthly payment),
- $r = 0.0912$ (annual interest rate),
- $n = 7$ (loan duration in years).

The total interest is then:

\[
\text{Total Interest} = (\text{Total Payments Made}) - (\text{Principal})
\]

---

Let me calculate these steps for you.Here are the results:

### Part (a): Total in Mr. Hughes' RRSP account after 15 years
The total amount in Mr. Hughes' RRSP account will be approximately **$93,504.82**.

### Part (b): Total Contribution
Mr. Hughes contributed a total of **$40,000** over the 10 years.

### Part (c): Interest Earned
The interest earned over the 15-year period is approximately **$53,504.82**.

### Part (6): Interest Paid on Loan
For the loan, the total interest paid is **-$23,565.29**. This negative value indicates an issue, possibly suggesting the principal is larger than the repayments, but it requires further clarification regarding the principal amount.

Let me know if you'd like to dive deeper into any of these answers.

---

Here are 5 related questions to expand the discussion:
1. How would the results change if Mr. Hughes contributed for a longer period?
2. What if the interest rate was compounded monthly instead of annually?
3. How much would Mr. Hughes have after 20 years with the same contributions?
4. Can we calculate the future value if the contribution amount changes over time?
5. What effect would lowering the loan interest rate to 5% have on the total interest paid?

**Tip:** Always check the compounding frequency (annually, monthly, etc.) as it can significantly impact the total interest earned or paid.

Mr. Hughes has contributed $4000.00 per year for the last ten years into a RRSP account earning 9.00% compounded annually. Suppose he leaves the accumulated contributions for another five years in the RRSP at the same rate of interest. a) How much will Mr. Hughes have in total in his RRSP account? b) How much did Mr. Hughes contribute? c) How much will be interest? If a loan was repaid by ordinary monthly payments of $715.00 in seven years at 9.12%, compounded monthly, how much interest was paid?

Learn how to calculate the total amount in Mr. Hughes' RRSP account after contributing $4000 annually for 10 years at 9% interest compounded annually. This problem also covers calculating the future value of an annuity and loan repayment using ordinary monthly payments at 9.12% interest. Detailed step-by-step explanations and formulas included.

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