Question

loan of EGP 80,000 is taken out. Interest payments are due every 3 months at j4= 10%. A sinking fund is set up to pay back the EGP 80,000 in one lump sum at the end of 5 years. The sinking fund earns j4 = 12 % and deposits are made quarterly. Find the quarterly debt expense.

Answer 1

Quarterly interest payment = Principal x rate x time

                                            = EGP 80,000 x 0.1 x 3/12

    = EGP 2,000

Quarter deposit for sinking fund can be computed using formula for FV of annuity as:

FV = P x [(1 + r) n – 1/r]

P = FV / [(1 + r) n – 1/r]

FV = Future accumulated value of deposits = EGP 80,000

P = Periodic cash flow

r = Rate of return = 0.012/4 = 0.03 quarterly

n = Number of periods = 5 x 4 = 20 periods

P = EGP 80,000/ [(1+ 0.03)20 – 1/r]

    = EGP 80,000/ [(1.03)20 -1/0.03]

    = EGP 80,000/ [(1.80611123466941-1)/0.03]

    = EGP 80,000/ (0.80611123466941/0.03)

    = EGP 80,000/ 26.8703744889804

    = EGP 2,977.25660774873 or EGP 2,977.26

Total quarterly debt expenses = EGP 2,000 + EGP 2,977.26 = EGP 4,977.26