SHR Incorporated borrowed $400,000. The company plans to set up a sinking fund that will pay back the loan at the end of 10 years. Assuming a rate of 6% compounded semiannually, the amount to be paid into the fund each period is (use the tables in the handbook):

To determine the periodic payment into the sinking fund required to pay back a loan of $400,000 in 10 years with an interest rate of 6% compounded semiannually, we can use the sinking fund formula:

\[ R = \frac{S \cdot i}{(1 + i)^n - 1} \]

where:
- $ R $ is the periodic payment.
- $ S $ is the future value, which is $400,000.
- $ i $ is the interest rate per period.
- $ n $ is the total number of periods.

Given:
- Annual interest rate ($ r $) = 6%
- Compounded semiannually, so $ i = \frac{r}{2} = \frac{6\%}{2} = 3\% = 0.03 $
- Number of years = 10, so $ n = 10 \times 2 = 20 $

Plugging the values into the formula, we get:

\[ R = \frac{400,000 \cdot 0.03}{(1 + 0.03)^{20} - 1} \]

First, let's calculate $(1 + 0.03)^{20}$:

\[ (1 + 0.03)^{20} = 1.03^{20} \approx 1.80611 \]

Now, calculate $(1.03^{20} - 1)$:

\[ 1.80611 - 1 = 0.80611 \]

Next, calculate the periodic payment $ R $:

\[ R = \frac{400,000 \cdot 0.03}{0.80611} \]

\[ R = \frac{12,000}{0.80611} \]

\[ R \approx 14,885.71 \]

So, the amount to be paid into the sinking fund each period is approximately $14,885.71.

Would you like more details or have any questions?

Here are 8 related questions that might interest you:

1. How is the formula for the sinking fund derived?
2. What happens if the interest rate changes during the investment period?
3. How would the payments change if the compounding was done annually instead of semiannually?
4. What is the impact of increasing the loan amount on the periodic payments?
5. How does the duration of the loan affect the amount to be paid into the sinking fund?
6. Can you show the calculations using different interest rates for comparison?
7. How is the sinking fund different from a regular savings account?
8. What are some practical applications of sinking funds in business finance?

**Tip:** Always double-check your financial calculations, especially when dealing with large sums or long periods, as small errors can accumulate and lead to significant discrepancies.

Learn how to calculate sinking fund payments required to repay a $400,000 loan in 10 years at a 6% annual interest rate compounded semiannually. Detailed step-by-step solution using the sinking fund formula. Suitable for financial professionals and advanced learners.

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