Question

Your company is planning to borrow $2.75 million on a 7-year, 15%, annual payment, fully amortized term loan. What fraction of the payment made at the end of the second year will represent repayment of principal? Round your answer to two decimal places.

Answer 1

Loan = $2.75 million = 2.75 x 1000000 = $2750000, No of years of loan = 7 years,

Annual interest rate = 15%

First we need to find the annual payment paid company on full amortizing loan. We can find the annual payment using PMT function in excel

Formula to be used in excel: =PMT(rate,nper,-pv)

Using PMT function in excel, we get annual payment of loan = 660990.9999

For year 1

Beginning loan balance = loan = 2750000,

Interest payment = Beginning loan balance x interest rate = 2750000 x 15% = 412500

Principal payment = Annual payment - interest = 660990.9999 - 412500 = 248490.9999

Ending balance = Beginning loan balance - Principal payment = 2750000 - 248490.9999 = 2501509.0001

For year 2 , Beginning Balance = Ending balance for year 1 = 2501509.0001

Interest payment = Beginning balance x interest rate = 2501509.0001 x 15% = 375226.3500

Principal payment = 660990.9999 - 375226.3500 = 285764.6499

Fraction of payment n second year that represent principal = Principal payment for year 2 / Annual payment = 285764.6499 / 660990.9999 = 43.2327% = 43.23% (rounded to two decimal places)

Hence Fraction of payment in second year that represents principal = 43.23%