Dean took out a 10-year loan for $40,000 at an APR of 4% compounded monthly. What will his balance be after he has made exactly half of his monthly payments

Answer:The balance be after he has made exactly half of his monthly payments is $56881.4.Step-by-step explanation:Given : Dean took out a 10-year loan for $40,000 at an APR of 4% compounded monthly.To find : What will his balance be after he has made exactly half of his monthly payments?Solution : Formula of monthly payment ,[tex]M=\frac{\text{Amount}}{\text{Discount factor}}[/tex]  Discount factor [tex]D=\frac{1-(1+i)^{-n}}{i}[/tex]  Where, Amount = $40,000Rate r= 4% compounded monthly[tex]i=\frac{4}{100}=0.04[/tex]  Time = 10 years  [tex]n=10\times12=120[/tex]  Now, put all the values we get,  [tex]D=\frac{1-(1+i)^{-n}}{i}[/tex]  [tex]D=\frac{1-(1+0.04)^{-120}}{0.04}[/tex]  [tex]D=\frac{1-(1.04)^{-120}}{0.04}[/tex]  [tex]D=\frac{1-0.00903}{0.04}[/tex]  [tex]D=\frac{0.9909}{0.04}[/tex]  [tex]D=24.7725[/tex]  [tex]M=\frac{\text{Amount}}{\text{Discount factor}}[/tex]  [tex]M=\frac{40000}{24.7725}[/tex]  [tex]M=1614.69[/tex]  Half of the monthly payment is $807.345Payment for 10 years is [tex]807.345\times 120=96881.4[/tex]The balance is $96881.4-$40000=$56881.4Therefore, The balance be after he has made exactly half of his monthly payments is $56881.4.