DQuestion 18 1 pts You get a loan for $100,000 today and will pay it back with y

Question

DQuestion 18 1 pts You get a loan for $100,000 today and will pay it back with yearly payments of $12,000 each year in years 1 to 7 In addition, you will make a single dollar payment in year 3 How big must the single payment be, if the loan charges 7.00% APR (compounded annually)? O The additional payment is equal to $43,279 O The additional payment is equal to $35,329 O The additional payment is equal to $64,671 O The additional payment is equal to $43,712 O The additional payment is equal to $42,413

Explanation / Answer

Present value of outflows=Cash outflows*Present value of discounting factor(rate%,time period)

=12000/1.07+12000/1.07^2+12000/1.07^3+x/1.07^3+...........+12000/1.07^7

100,000 =12000/1.07+12000/1.07^2+12000/1.07^3+x/1.07^3+...........+12000/1.07^7[where x=cash flow for year3]

100,000=12000[1/1.07+1/1.07^2+.............+1/1.07^7]+x/1.07^3

100,000=12000*5.389289402+x*0.816297876

Hence x=(100,000-64671.47282)/0.816297876

=$43279(Approx).

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