calculus
posted by molly anne on .
Assume your business associate owes you $13650. Also assume they offer either $12020 now or $ 1950 per year for 7 years, starting now. Assume a 5.6% market interest rate, compounded continuously.
How much would you have at the end of 7 years if you choose to
take the $12020 offer now, and you use the market to earn interest
on the funds?
How much would you have at the end of 7 years if you choose to
take the installments each year, and you still used the market to earn
interest on the the funds?

Pt = Po * e^(r*t).
Pt = value after time t.
Po = Initial investment.
e = 2.7183 = base of natural log.
r = Annual percentage rate(APR).
t = lengtth of investment in years.
First Option
Pt = 12020 * 2.7183^(0.056*7) = 17788.90.
2nd Option
Year 1. Pt = 1950 * 2.7183^(0.056*1) = 2062.32 @ end of 1st yr.
2. Pt = (2062.32 + 1850) * 2.7183^(0.056*1) = 4243.42 @ end of 2nd yr
3. Pt = (4243.42 + 1950) * 2.7183^(0.056*1) = 6550.15 @ end of 3rd yr
4. Pt = (6550.15 + 1950) * 2.7183^(0.056*1) = 8989.74 @ end of 4th yr
5. Pt = (8989.74 + 1950) * 2.7183^(0.056*1) = 11569.85 @ end of 5th yr
6. Pt = (11569.85 + 1950) * 2.7183^(0.056*1) = 14298.57 @ end of 6th yr
7. Pt = (14298.57 + 1950) * 2.7183^(0.056*1) = 17184.46 @ end of 7th yr
Option 1(17788.90) is the best choice.
NOTE: Under option 2, interest was earned on the interest.