question archive Exactly seven years ago, Xen borrowed $325,000 to buy a house
Exactly seven years ago, Xen borrowed $325,000 to buy a house
Subject:FinancePrice:3.87 Bought7
Exactly seven years ago, Xen borrowed $325,000 to buy a house. The fixed annual interest rate on the 30-year loan is 4.90% p.a. The loan requires monthly payments, the first payment was made exactly one month after Xen bought the house, and Xen has made every payment for the past seven years on time. Because interest rates have recently decreased, Xen is considering refinancing the loan. Assuming that Xen just made the 84th payment on the loan, what is the remaining balance on the loan (i.e., the amount that Xen would need to refinance to completely pay off the current loan)? 1) $271,367.55 2) $285,236.60 3) $278,361.82 4) $266,147.84 5) $291,783.29
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Answer
| Loan Amount | $ 325,000.00 |
| Interest Rate(4.90%/12) | 0.004083333 |
| Time Period(12*30) | 360 |
| Present Value Factor | (1-((1+r)^-t)/r) |
| PVF r = 0.0040833 and t = 360 | 188.420888 |
| Monthly Payment(Loan Amount/PVF) | $ 1,724.86 |
| OR | |
| Monthly Payment using PMT | $ 1,724.86 |
Now we need to calculate principal amount remaining at the end of 84th payment or in the beginning of 85th payment. The period will be given by 360-85+1 = 276. we shall multiply PVF of r = 0.0040833 and t = 276 with the monthly payment to find the principal amount.
| PVF(r = 0.0040833, t = 276) | 165.3677973 |
| Principal Amount after 84th payment | $ 285,236.60 |
Hence, the correct option is 2) $285,236.60
