Anderson takes out a loan of $22,000 at j₁₂ = 9% to be repaid over 5 years with monthly payments.After 24 payments,the outstanding balance on the loan is $14,361.35,but Anderson misses the next 10 monthly payments.At the end of the 34^th month,he makes a lump sum payment of $3000 and refinances the loan such that he still pays off the loan at the end of 5 years.If the interest rate is unchanged,what is the new monthly payment (first payment made at time 35)?

Question

Quizplus · Accepted Answer

We can use the formula for the present value of an annuity to find the monthly payment that Anderson should be making in order to pay off the loan at the end of 5 years:
PV = PMT*((1-(1+i)^(-n))/i)
where PV is the present value (or outstanding balance) of the loan, PMT is the monthly payment, i is the monthly interest rate, and n is the number of payments remaining.
Using the values given in the problem:
PV = $14,361.35
i = 0.09/12 = 0.0075
n = (5-3.5)*12 = 18
Substituting these values into the formula and solving for PMT, we get:
$14,361.35 = PMT*((1-(1+0.0075)^(-18))/0.0075)
PMT = $529.92 (rounded to the nearest cent)
However, Anderson missed 10 payments, so his outstanding balance after 34 months would have been higher than $14,361.35 if not for the lump sum payment of $3000. We can use the same formula to calculate this higher outstanding balance:
PV = PMT*((1-(1+i)^(-n))/i) + FV*(1+i)^(-n)
where FV is the future value of the lump sum payment (which we will assume is not subject to interest), and n is the number of payments remaining from the point at which Anderson missed his payments.
Using the values given in the problem:
FV = $3000
n = (5-3.5)*12-10 = 2
Substituting these values into the formula and solving for PV, we get:
PV = $17,756.17
This is the outstanding balance that Anderson had at the end of the 34th month. We can now use the same formula as before to calculate the new monthly payment:
$17,756.17 = PMT*((1-(1+0.0075)^(-30))/0.0075)
PMT = $519.04 (rounded to the nearest cent)
Therefore, the answer is C ($529.92).

Anderson Takes Out a Loan of $22,000 at J12 =

Anderson Takes Out a Loan of $22,000 at J₁₂ =