10 3. (Example 6-2) John owes Jane $10,000 on a note which is due in five years
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Question
10
3. (Example 6-2) John owes Jane $10,000 on a note which is due in five years with accumulated interest at 6%. Jane has an investrment opportunity now that he thinks will eam 18%. There's a chance, however, that it will eam as little as 3 A bank has offered to discount the note at 12% and give Joe cash that he can invest today. a. How much ahead will Jane beif he takes the bank's offer and the investrment does tum out to yield 18%? b. How much behind will she be if the investrment tums out to yield only 3%?Explanation / Answer
a) If Jane takes the Bank's offer and the investment earns 18%:
Money Received after discounting: 10,000 - (10,000 x 12%) = $8,800
If investment earns a return of 18% for 5 Years than after 5 Years, Investment value will be:
A = P (1+ r/n) nt
A = Future Value, P = Principal = 8,800, r = Interest Rate = 18%, n = Compounding Frequency = 1, t = Time in Years = 5
A = 8,800 ( 1 + 0.18 / 1) 5x1
A = $20,132.27
Total Value of Investment = $20,132.27
If Jane does not discount it with Bank than:
A = 10,000 ( 1 + 0.06 / 1) 5x1
Value of Note = $13,382.26
Jane will be ahead by: 20,132.27 - 13,382.26 = $6,750
b) If Jane takes the Bank's offer and the investment earns 3%:
Money Received after discounting: 10,000 - (10,000 x 12%) = $8,800
If investment earns a return of 3% for 5 Years than after 5 Years, Investment value will be:
A = P (1+ r/n) nt
A = Future Value, P = Principal = 8,800, r = Interest Rate = 3%, n = Compounding Frequency = 1, t = Time in Years = 5
A = 8,800 ( 1 + 0.03 / 1) 5x1
A = $10,201.61
Total Value of Investment = $10,201.61
If Jane does not discount it with Bank than:
A = 10,000 ( 1 + 0.06 / 1) 5x1
Value of Note = $13,382.26
Jane will be behind by: 10,201.61 - 13,382.26 = -$3,180.65
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