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# Math 12

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In 2008 a major bank in the US borrowed 10 million dollars for the US government at an annual rate of 0.50% compounded annually. They then used that money to purchase US government 30 year bonds (investment) that yields 4.65% compounded annually? How much did this cost the US taxpayers in the first year? [It will be the profit the bank makes] (use your financial application and fill in the appropriate inputs)

Interest paid by Bank

Interest earned by Bank.

I need help asap!

May 6, 2021

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Well, FV (future value) & PV (present value) are related as follows:

$$FV = PV (1 + r)^t$$

And interest is really just the future value of an investment minus the present value. r is your rate, t is the time that passed, which is conveniently 1 in this example.

Thus your increase due to interest is $$1+r , or, 1.005$$ (since we have to divde percentages by 100).

$$10,000,000 * 1.005 =10,050,000$$

$$10,050,000 - 10,000,000 = 50,000$$

^ Interest paid by the bank

The second half could be done the very same way. Or, we can notice that since only 1 year passed and the interest is calculated annually, we can skip some steps and just multiply the interest rate by the present value:

$$10,000,000 \times .0465 = 465,000$$

As is typically, the bank is pulling one over on the US gov't. That deal cost \$415,000!

If you're ever doing "net" costs like this, it might be helpful to know you can skip one more step and just subtract the two rates from each other before multiplying by your present value (or principle):

$$10m \times .0465 - 10m \times .005 = 10m (.0465 - .005)$$

May 6, 2021