Question

You want to invest $15,000 in government securities for the next two years. You can either invest in a security that pays an interest rate of 7.5% per year for the next two years, or invest in a security that matures in one year but pays 5.5%. If you decide to invest in the security that matures in one year, you would then reinvest your savings for another one year. What should be the one year interest rate next year which will make the future value equal for both securities?

		9.54%
		9.47%.
		9.42%.
		9.51%.

Answer 1

The one year interest rate next year which will make the future value equal for both securities is calculated as shown below:

Future value of $ 15,000 if invested at 7.5% per year for 2 years is computed as follows:

Future Value = Present Value ( 1 + r )ⁿ

= $ 15,000 ( 1 + 0.075 )²

= $ 17,334 Approximately

Future Value of $ 15,000 if invested for 1 year at rate of interest of 5.5% is computed as follows:

= $ 15,000 ( 1 + 0.055 )¹

= $ 15,825

Now we shall be using the below equation in order to find out the rate of interest that will equate the future value:

$ 17,334 = $ 15,825 ( 1 + r )¹

If we plug in r = 9.54% it will approximately be equal to the future value of $ 17,334.

Hence the correct answer is option a i.e. 9.54%

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