Isabelle takes out a loan of $15000 to buy a car. She pays the loan back in monthly instalments over 5 years. The nominal annual interest rate is 6.8%, compounded monthly.
(a) Calculate the value of Isabelle’s monthly repayment. [3]
(b) Calculate the total amount Isabelle pays back over the 5 years. [2]
(c) Calculate the total interest Isabelle pays on the loan. [1]
After 2 years (24 payments), Isabelle considers refinancing the loan.
(d) Calculate the amount of the loan that Isabelle still owes immediately after her 24th payment. [3]
She finds a new loan offer for the remaining amount at a nominal annual interest rate of 5.2%, compounded monthly, to be paid back over the remaining 3 years.
(e) Calculate her new monthly repayment amount if she accepts this offer. [3]
(f) Calculate the total amount Isabelle will save over the remaining 3 years by refinancing the loan. [4]
Question
Calculate the value of Isabelle’s monthly repayment. [3]
Hint
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Hint
Use the TVM calculator with N = 60, I% = 6.8, PV = 15000, and FV = 0 to determine the monthly payment.
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Calculate the total amount Isabelle pays back over the 5 years. [2]
Hint
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Multiply the monthly repayment by 60 (the total number of payments).
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Complete Answer
$17735.40
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Question
Calculate the total interest Isabelle pays on the loan. [1]
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Subtract the original loan amount from the total amount paid.
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Calculate the amount of the loan that Isabelle still owes immediately after her 24th payment. [3]
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Use the TVM solver with N = 24, I% = 6.8, PV = 15000, and PMT = -295.59 to calculate the remaining balance.
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Calculate her new monthly repayment amount if she accepts the new loan offer. [3]
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Using the remaining balance as the principal, set N = 36, I% = 5.2, and compute the new PMT.
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Calculate the total amount Isabelle will save over the remaining 3 years by refinancing the loan. [4]
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Compute the cost of the remaining payments under both the original and refinanced schemes, then find the difference.
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