Posted by molly anne on Thursday, September 16, 2010 at 4:36pm.
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?

calculus  Henry, Friday, September 17, 2010 at 12:10pm
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.
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