Question

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2) A debt of $32 000 is repaid by payments of $2950 made at the end of every six months. Interest is 8.28% compounded quarterly. a. What is the number of payments needed to retire the debt? b. What is the cost of the debt for the first five years? c. What is the interest paid in the 10th payment period? d. Construct a partial amortization schedule showing details of the first five payments.

Answer 1

Question a:

Quarterly interest rate = 8.28% / 4 = 2.07%

r = Six months interest rate = (1+2.07%)^2 - 1 = 1.04182849 - 1 = 0.04182849 = 4.1828%

P = Semi annual payment = $2,950

PV = Debt value = $32,000

Payment = [r * PV] / [1 - (1+r)^-n]

$2,950 = [4.1828% * $32,000] / [1 - (1+4.1828%)^-n]

$2,950 = $1,338.496 / [1 - (1.041828)^-n]

1 - (1.041828)^-n = 0.453727458

(1.041828)^-n = 0.546272542

(1.041828)^n = 1.83058807

n = 14.754

Therefore, 15 payments needed to retire tha debt

Question b:

Cost of Debt for first five periods = (Total interest paid ) / Total debt

= ($1,338.496 + $1,271.090 + $1,200.864 + 1,127.702 + $1,051.479) / $32,000

= $5,989.63 / $32,000

= 0.187176

Question c:

Interest paid in 10th period is $619.79

Question d:

Amortization Schedule:

Period Opening Balance Installment payment Interest paid Principal amount repaid Closing Balance D=B*4.1828% E = C-D FEB-E 32000 2950 1338.496 1611.504 30388.496 30388.496 2950 1271.090011 1678.909989 28709.58601 28709.58601 2950 1200.864564 1749.135436 26960.45057 26960.45057 2950 1127.701727 1822.298273 25138.1523 25138.1523 2950 1051.478634 1898.521366 23239.63094 23239.63094 2950 972.0672828 1977.932717 21261.69822 21261.69822 2950 889.3343131 2060.665687 19201.03253 19201.03253 2950 803.1407887 2146.859211 17054.17332 17054.17332 2950 713.3419616 2236.658038 14817.51528 14817.51528 2950 619.7870292 2330.212971 12487.30231