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Answer: Borrow at the 3-year spot rate and lend at the 4-year spot rate to earn a return of GBP 28,000.
The treasurer of the London-based insurance company is looking to lock in a rate of return on a future receipt of GBP 800,000, which is expected to be received in 3 years. The treasurer plans to invest this amount for an additional year at today's forward rate. The current spot rates for 3 years and 4 years are 1.5% and 2%, respectively, with continuous compounding assumed. To determine the forward rate for the period from the end of year 3 to the end of year 4, we can use the formula: \[ F = \frac{(1 + T_2)^n - (1 + T_1)^m}{T_2 - T_1} \] where \( F \) is the forward rate, \( T_1 \) and \( T_2 \) are the spot rates for the two periods, and \( m \) and \( n \) are the number of years for each period. Plugging in the values: \[ F = \frac{(1 + 0.02)^4 - (1 + 0.015)^3}{4 - 3} \] Simplifying, we get: \[ F = \frac{(1.02)^4 - (1.015)^3}{1} \] \[ F = \frac{1.082432 - 1.047625}{1} \] \[ F = 0.034807 \text{ or } 3.48\% \] This calculation gives us the annualized forward rate for the period from year 3 to year 4. However, the explanation in the file content uses a simplified approach to find the forward rate, which results in a slightly different rate of 3.5%. This discrepancy could be due to rounding or a different method of calculation. Using the simplified forward rate of 3.5%, the treasurer can earn an interest income of GBP 28,000 on the GBP 800,000 by borrowing at the 3-year spot rate of 1.5% and lending at the 4-year spot rate of 2%. This is because the effective rate earned on the investment is the difference between the 4-year spot rate and the 3-year spot rate, compounded over the period. The correct answer is A: Borrow at the 3-year spot rate and lend at the 4-year spot rate to earn a return of GBP 28,000. This strategy allows the treasurer to lock in the forward rate and earn the desired return on the future receipt of funds.
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The finance director of an insurance firm headquartered in London anticipates receiving a sum of GBP 800,000 three years from the current date. With the intention of investing these funds for an additional year post that period, the finance director has made the decision to secure a predetermined rate of return on the investment, based on the prevailing forward rate for that specific timeframe.
Given the current financial environment:
The company has the capacity to both borrow and lend at these rates. Furthermore, we will use the assumption of continuous compounding to calculate the interest income and necessary financial transactions.
What will be the amount of interest income generated by the company during the 1-year timeframe starting from three years hence? Additionally, what financial transactions should the finance director undertake today to secure this rate of return?
A
Borrow at the 3-year spot rate and lend at the 4-year spot rate to earn a return of GBP 28,000.
B
Lend at the 3-year spot rate and borrow at the 4-year spot rate to earn a return of GBP28,000
C
Borrow at the 3-year spot rate and lend at the 4-year spot rate to earn a return of GBP 28,119.
D
Lend at the 3-year spot rate and borrow at the 4-year spot rate to earn a return of GBP 28,119.