Question

16. Your company borrowed $125 million from a Bank on December 31 2017 for one year at a fixed interest rate of 3%. It amortizes 50% after six months. Interest is paid semi-annually. Your two payments to the bank this year are:

a) $64,385,417 & $63,458,333

b) $64,385,417 & $63,416,667

c) $64,375,000 & $64,375,000

d) $64,375,000 & $63,437,500

Answer 1

Solution :

Calculation of First Payment to the Bank :

a. Interest amount payable

As per the information given in the question we have

Principal amount borrowed = 125,000,000   ;   Annual Interest Rate = 3 % =0.03

Thus Semi annual Interest Rate = Annual Interest rate / 2 = 0.03 /2 = 0.015

Thus Interest paid in the first six months = Total Principal amount * Semiannual Interest Rate

= 125,000,000 * 0.015 = $ 1,875,000 --------- (A)

Principal amount repaid in the first six months = $ 62,500,000 --------- (B)

Thus the total amount of First payment made = Principal Repayment / amortization + Interest payment

= (A) + (B)

= $ 62,500,000 + $ 1,875,000

= $ 64,375,000

The first payment made to the bank = $ 64,375,000

Calculation of Second Payment to the Bank :

a. Interest amount payable

As per the information given in the question we have

Principal amount borrowed = 125,000,000 ; Principal repaid / amortized in the first six months = $ 62,500,000

Balance of principal amount to be repaid = Principal amount borrowed – Principal repaid or amortized in the first six months

= $ 125,000,000 - $ 62,500,000

= $ 62,500,000

Semiannual Interest Rate = Annual Interest rate / 2 = 0.03 /2 = 0.015

Thus Interest paid in the next six months = Balance Principal amount * Semiannual Interest Rate

= 62,500,000 * 0.015 = $ 937,500 --------- (A)

Principal amount repaid in the next six months = $ 62,500,000       --------- (B)

Thus the total amount of second payment made = Balance Principal Repayment / amortization + Interest payment

= (A) + (B)

= $ 62,500,000 + $ 937,500

= $ 63,437,500

The second payment made to the bank = $ 63,437,500

Thus the first payment made to the bank = $ 64,375,000

Thus the second payment made to the bank = $ 63,437,500

The solution is Option d) $64,375,000 & $63,437,500