Final answer:
An increase in a short-term investment balance by $10,000 does not provide enough detail to determine the reason for the change without additional context. The value paid for a bond fluctuates with interest rate changes - if rates fall, bond prices rise, and vice versa. Calculating the initial deposit needed for a future value involves using the formula for compound interest to work backwards from the desired future amount.
Step-by-step explanation:
The situation described suggests that Pernell Company's increase of $10,000 in its short-term investment account could be due to a variety of factors. However, without specific details about the cause of the increase, such as whether the company made new investments or whether existing investments appreciated in value, it is impossible to determine the exact reason for the change. If interest rates have changed, and assuming the short-term investment might be bonds, the value paid for the bond would depend on whether interest rates have risen or fallen. If rates have fallen, the price of existing bonds would increase, so you would expect to pay more than $10,000 for a bond paying a fixed interest rate that was higher than the new lower market rates. Conversely, if rates have risen, existing bonds would decrease in value, and you might pay less than $10,000 for a bond paying a fixed interest rate that is now lower than new market rates. For example, with Singleton Bank's balance sheet changes presented in the question, we can see that the bank altered its assets and liabilities without specific details about interest rates changes. However, we can deduce from the provided example that if Singleton decided to purchase bonds at $10,000 each, changes in interest rates would affect the price of these bonds as mentioned previously.
In terms of calculating an initial investment for future value under compound interest, the formula we would use is P = A / (1 + r/n)^(nt), where P is the principal amount (initial investment), A is the future value, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years. Using the specific example to have $10,000 in ten years with a 10% interest rate compounded annually (n=1 in this case), the calculation would be P = $10,000 / (1 + 0.10/1)^(1*10), which simplifies to P = $10,000 / (1.10)^10.