Question 17 1 pts You get a loan for $100,000 today and will pay it back with ye

Question

Question 17 1 pts You get a loan for $100,000 today and will pay it back with yearly payments of $10,000 each year in years 1 to 10. In addition, you will make a single dollar payment in year 3 How big must the single payment be, if the loan charges 5.00% APR (compounded annually)? O The additional payment is equal to $26,374 O The additional payment is equal to $22,783 O The additional payment is equal to $77,217 O The additional payment is equal to $26,638 O The additional payment is equal to $25,846

Explanation / Answer

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

=10,000/1.05+10,000/1.05^2+10,000/1.05^3+x/1.05^3+........+10,000/1.05^10

100,000 =10,000/1.05+10,000/1.05^2+10,000/1.05^3+x/1.05^3+........+10,000/1.05^10[where x=cash outflow for year 3]

100,000=10,000[1/1.05+1/1.05^2+1/1.05^3+...........+1/1.05^10]+x/1.05^3

100,000=10,000*7.721734929+x*0.863837598

Hence x=(100,000-77217.34929)/0.863837598

which is equal to=$26374(Approx).

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