# calculus

Choice 1: Payments of \$ 2600 now, \$ 3200 a year from now, and \$ 3880 two years from now.
Choice 2: Three yearly payments of \$ 3200 starting now.
Modification: Interest is compounded continuously instead of annually.

(a) If the interest rate on savings were 4.86 %, which would you prefer?
(Type in 1 for Choice 1, or 2 for Choice 2.)
(b) What is the interest rate that would make both choices equally lucrative?

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1. a.) choice 1

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2. Assuming choices are payment options, i.e. we will be paying the said amounts.

Total amount of payment for each choice is \$9600.
Assuming we have \$9600 in the bank, we calculate what would we have accumulated in interest at the end of two years.

Choice 1:
3800 for 2 years +
3200 for 1 year.
Interest at annual rate 4.86%
=3800*1.0486²-3800+3200*0.0486
=533.86

Choice 2:
3200 for 2 years + 3200 for 1 year
Interest at continuous rate of 4.86%
=3200(e^(.0486*2))-3200+3200(e^(.0486))-3200
=486.02

So the first choice is more profitable.

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