The problem is about calculating the future value of an annuity and additional inheritance compounded over time.

Let's break it down:

1. Part (a): Nick has been making monthly deposits of $110 for 35 years (or 420 months), with a 7% annual interest rate compounded monthly.

   The formula to calculate the future value of an annuity is:

   $A = P \times \frac{(1 + r)^n - 1}{r}$

   where:

   • $P$ is the monthly deposit ($110),
   • $r$ is the monthly interest rate (7% annual rate means $\frac{7}{12 \times 100} = 0.0058333$ per month),
   • $n$ is the total number of months (35 years = 420 months).

2. Part (b): Nick received an inheritance of $15,000 10 years ago, which he deposited into the same retirement fund. We need to find the future value of this lump sum after 10 years with the same 7% interest rate compounded monthly.

   The formula to calculate the future value of a lump sum is:

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

   where:

   • $P$ is the lump sum ($15,000),
   • $r$ is the monthly interest rate (0.0058333),
   • $n$ is the total number of months (10 years = 120 months).

The answers provided are:

• $\text{Part (a)}: \, A = 198,116.01$
• $\text{Part (b)}: \, A = 27,321.83$

Do you need further explanation on the calculations? If so, let me know!

Here are some follow-up questions:

1. How does increasing the interest rate affect the accumulated amount in an annuity?
2. What happens to the future value if Nick deposited $150 instead of $110 monthly?
3. How would the calculations change if the interest was compounded quarterly instead of monthly?
4. How would delaying the inheritance deposit by 5 years impact the future value in Part (b)?
5. What formula would you use if the interest was compounded continuously?

Tip: Always break compound interest problems into smaller steps to ensure precision!