Suppose that your college offers you two payment plans. You may either pay tuition of $10,000 per year at the beginning of each of the next four years, or pay just $38,000 before the start of freshman year. If the interest rate is 10%, what would you do? If the interest rate were 2%, what would you do? Intuitively explain the difference in your answer
What will be an ideal response?
At 10%, the future stream of tuition payments is worth:
$10,000 ? [1 + 1/(1.10 ) + 1/(1.10)2 + 1/(1.10)3] = $10,000 ? [1 + .9091 + .8264 + .7513] = $34,868
At 2%, the future stream of tuition payments is worth:
$10,000 ? [1 + 1/(1.02 ) + 1/(1.02)2 + 1/(1.02)3] = $10,000 ? [1 + .98 + .961 + .9425] = $38,835
Thus, if the interest rate is 10%, paying each year costs less and is preferred to the up-front payment of $38,000. If the interest rate is 2%, the up-front payment costs less than paying each year. Intuitively, compared to 10%, the university's discount is not a good deal, but compared to 2% it is. Alternatively, when the interest rate is 10%, one can save the $38,000 instead of paying it up front and come out ahead.
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