Find the periodic payment r required to accumulate a sum of s dollars over t year with interest earned at the rate%/year compounded m times a year. P=180000, r=11.5, t=30, m=12

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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Find the periodic payment r required to accumulate a sum of s dollars over t years with interest earned at the rate%/year compounded m times a year. P=180000, r=11.5, t=30, m=12

Learn how to calculate the periodic payment required to accumulate a sum of $180,000 over 30 years with a 11.5% interest rate compounded 12 times a year. This solution uses the future value of an annuity formula and explains each step in detail. Suitable for college-level finance and mathematics students.

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