Question

Suppose 2 years ago a borrower borrowed a FRM loan at 12% IRR with monthly payments for an initial balance of $100000 with 20 years term. Further suppose that the current interest rate available in the market is 6%. the borrower could refinance the loan at 6% interest but keep the same monthly payments and reduce the number of months needed to amortize the debt. What will be the new months needed to amortize the debt?

*Please show work on by using a financial calculator and formula, not by Excel sheet.

Answer 1

Current monthly payment can be calculated using PMT function on a calculator

N = 20 x 12 = 240, PV = 100,000, I/Y = 12%/12 = 1%, FV = 0

=> Compute PMT = $1,101.09

Let's calculate the outstanding debt amount today using the following formula

FV = PV x (1 + r)^n - P / r x ((1 + r)^n - 1)

where, PV - Original Loan amount = 100,000, r - interest rate = 1%, n - no. of payment = 2 x 12 = 24, P - Monthly payment = 1,101.09

=> Outstanding Loan, FV = 100,000 x (1 + 1%)^24 - 1,101.09 / 1% x (1.01^24 - 1) = $97,273.36

No. of months can be calculated using N function

I/Y = 6%/12 = 0.5%, PV = 97,273.36, FV = 0, PMT = -1,101.09

=> Compute N = 117 months.