Sandy takes out a loan of $22,000 at j₁₂ = 9%,repaid over 5 years with monthly payments.After 24 payments,the outstanding balance on the loan is $14,361.35.Just after the 24^th payment,Sandy makes a lump sum payment of $3000 and refinances the loan with monthly payments for two more years at the same interest rate.What is the new monthly payment?

Question

Quizplus · Accepted Answer

Using the loan formula, we can calculate the original monthly payment of Sandy's loan:

PV = 22000
n = 5*12 = 60
i = 9%/12 = 0.75%

PMT1 = i*PV / (1 - (1 + i)^(-n)) = $464.80

After 24 payments, the remaining balance is $14,361.35. We can use this information to find the remaining balance after 36 payments:

PV2 = 14361.35
n2 = 36
i2 = 9%/12 = 0.75%

PMT2 = i2*PV2 / (1 - (1 + i2)^(-n2)) = $405.53

However, after the 24th payment, Sandy makes a $3000 lump sum payment. So, the remaining balance after the lump sum payment is:

PV2' = PV2 - $3000 = $11361.35

Now, Sandy refinances the remaining balance over 24 months, with the same interest rate of 9%. Let's call the new monthly payment PMT3. Using the loan formula again, we can solve for PMT3:

PV3 = 11361.35
n3 = 24
i3 = 9%/12 = 0.75%

PMT3 = i3*PV3 / (1 - (1 + i3)^(-n3)) = $519.04

Therefore, the new monthly payment is $519.04. Answer choice C is correct.

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

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