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A note for \$250 dated August 1st 2010, is due with compound interest at $i=9\%$, 4 years after date. On November 1st 2011, the holder of the note has it discounted by a lender who charges $i=7.5\%$. What are the proceeds?

So the way I approached this was I took the \$250 as the present value on August 2010, and found the future value up to November 2011 at the 9% rate:$$A(t)*(1+i)^{-t}=250*(1.09)^{-1.25}=224.47$$Where $i=9\%$ and $t=time\space in \space years=\frac{15}{12}=1.25$. Then I took this value as my new present value on November 2011, and found the new future value up to August 2014 at the discounted 7.5% rate:$$224.47*(1.075)^{-2.75}=183.99$$Where $i=7.5\%$ and $t=\frac{33}{12}=2.75$. The answer at the back of the book however, is $289.25. How did they arrive at this value? Thanks a lot.

Random Student
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1 Answers1

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The future value for the first step should be:

$$A*(1+i)^{t}=250*(1.09)^{1.25}=278.43 \; .$$

What you computed is present value. See the difference?

Secondly, what you want is the future value for 4 years. Not just up till November 2011. Then you discount from there to November 2011 with the other rate, which gives:

$$250*(1.09)^4 * (1.075)^{-2.75} = 289.25 \; .$$

Raskolnikov
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