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!

Guest May 6, 2021

#1**0 **

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):

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

Guest May 6, 2021