*Problem 5.11 Your brother has asked you for a loan and has promised to pay back

Question

*Problem 5.11 Your brother has asked you for a loan and has promised to pay back $8,450 at the end of three years. If you normally invest to earn 7 percent per year, how much will you be willing to lend to your brother? (If you solve this problem with algebra round intermediate calculations to 4 decimal places, in all cases round your final answer to the nearest penny.) Amount to be invested today Question Attempts: 0 of 3 used Copyright © 2000-2015 by John Wiley Sons. Inc. or related companies All nghts reserved

Explanation / Answer

Let the amount lend be "x"

Interest rate = 7%

Interest at the end of 1st year = 0.07x

Total amount at the end of 1st year = x+0.07x = 1.07x

Interest for 2nd year = amount at the end of 1st year*7% = 1.07x*0.07 = 0.0749x

Amount at the end of 3rd year = 1.07x+0.0749x = 1.1449x

Interest for 3rd year = 0.07*1.1449x = 0.080143x. Amount at the end of 3rd year = 1.1449x+ 0.080143x = 1.2250x

So, 1.2250x = 8450

or x = 8450/1.2250 = $6,898 (rounded off). This is the amount that will be lend.

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