Ken loans his grandson rex $20,000 at 5.5 percent per year to help pay for execu
ID: 1092319 • Letter: K
Question
Ken loans his grandson rex $20,000 at 5.5 percent per year to help pay for executive chef schoolingg in Florida . Rex requires 3 years till he begins to earna a salary. he agrees to pay ken the loan in the following order : year 1,2,3 nothing to be paid year 4 : X, year 5 : 2X, year 6 : 3X, year 7 : 4X, year 8 : 5X
a) Find the value of X such that the loan is fully repaid with the last payment.
b) What is the dollar amount of each of the five payments ?
c) Find the value of all the intrest paid to ken ?
Explanation / Answer
a.
Total PV of future payments= 0.8072x + 0.765*2x + 0.7252 * 3x + 0.6874 *4x + 0.6516 * 5x = 10.5209x
This should equal 20000
Thus, 10.5209x = 20000
x = 20000/10.5209 = $1,900.97
b.
c. Total amount paid over the 8 years = 28514.50
Thus value of total interest paid = 28514.50 - 20000 = $8,514.50
Year PV of $1 at 5.5% interest CF 0 1 -20000 1 0.947867299 0 2 0.898452416 0 3 0.851613664 0 4 0.807216743 x 5 0.765134354 2x 6 0.725245833 3x 7 0.687436809 4x 8 0.651598871 5xRelated Questions
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