We can use the future value of an annuity formula to determine the periodic payment $r$ required to accumulate a sum of money. The formula is:

$S = r \times \frac{(1 + i)^n - 1}{i}$

Where:

• $S$ is the future value or the accumulated amount (not given here, but will be related to $P$, the present value),
• $r$ is the periodic payment,
• $i = \frac{r}{m}$ is the interest rate per period,
• $n = m \times t$ is the total number of periods (compounded times per year multiplied by the number of years),
• $P$ is the present value or loan amount (given as 180,000),
• $t$ is the time in years (given as 30 years),
• $m$ is the number of compounding periods per year (given as 12),
• $r$ is the annual interest rate divided by the number of periods.

Here we have $P = 180,000$, $r = 11.5\% = 0.115$, $t = 30$, and $m = 12$.

Let's first calculate the periodic rate $i$ and the total number of periods $n$:

$i = \frac{r}{m} = \frac{0.115}{12}$ $n = m \times t = 12 \times 30$

Now we substitute into the formula to calculate $S$, the future value.

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