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Mental mathHard

A desk borrows $50000000$ at an annual rate of $4.20%$ and lends the same amount at an annual rate of $4.55%$ , both for the same $90$ days. Use a $360$ -day year and simple interest. What is the desk's net interest income over the $90$ days?

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Hint

Work with the spread between the rates, then prorate for the period.

Solution

The spread is $4.55% - 4.20% = 0.35%$ , i.e. $35$ basis points.
Annual net interest is $0.0035 \times 50000000 = 175000$ .
The period is $90 \div 360 = \frac{1}{4}$ of a year.
So the income is $175000 \div 4 = 43750$ .

Answer: $43750$

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