Mark borrowed an amount of P8,830 from Brian and after 2 years, he borrowed again an amount of P2,750.

Question

Mark borrowed an amount of P8,830 from Brian and after 2 years, he borrowed again an amount of P2,750. He paid P3,600 one year after the last borrow, P2,450 the following year, and P1,800 the next year after. If the money is worth 9.45% compounded semi-quarterly, determine the following:

1. Amount he should pay 7 years after the last borrow to discharge all his debts.

2. Amount he should pay as a single lump sum at the end of 6th year to discharge all his debts.

Answer 1

Question 1: Payment 7 years after last borrow (Year 9)

Focal date: Year 9 (18 half-year periods from year 0)

Future value of borrowings:

First borrow: 8,830(1.04725)^18 = 8,830 × 2.2811 = P20,141.86

Second borrow: 2,750(1.04725)^14 = 2,750 × 1.9027 = P5,232.41

Total borrowed: P25,374.27

Future value of payments:

Payment 1: 3,600(1.04725)^12 = 3,600 × 1.7369 = P6,252.88

Payment 2: 2,450(1.04725)^10 = 2,450 × 1.5851 = P3,883.48

Payment 3: 1,800(1.04725)^8 = 1,800 × 1.4461 = P2,603.05

Total payments: P12,739.41

Final payment = 25,374.27 - 12,739.41 = P12,634.86

Question 2: Single lump sum at end of 6th year

Focal date: Year 6 (12 half-year periods from year 0)

Future value of borrowings:

First borrow: 8,830(1.04725)^12 = 8,830 × 1.7369 = P15,337.01

Second borrow: 2,750(1.04725)^8 = 2,750 × 1.4461 = P3,976.88

Total borrowed: P19,313.89

Future value of payments:

Payment 1: 3,600(1.04725)^6 = 3,600 × 1.3190 = P4,748.51

Payment 2: 2,450(1.04725)^4 = 2,450 × 1.2028 = P2,946.96

Payment 3: 1,800(1.04725)^2 = 1,800 × 1.0967 = P1,974.13

Total payments: P9,669.60

Single payment = 19,313.89 - 9,669.60 = P9,644.29