Question

11) A debt of $10,000 with interest at 8% compounded quarterly is to be repaid by equal payments at the end of every six months for two years.

a) Calculate the size of the semi-annual payments.

b) Construct an amortization table for the complete 2 years with dollar amounts to two decimal places i.e. include the pennies. Round your semi-annual payment to the next higher dollar. If you did not get an answer to part a), assume a debt of 20,000, a rate of 10% and a semi-annual payments of $5,650 for 2 years.

c) Calculate the outstanding balance after three payments using formulas.

Answer 1

Question a:

Quarterly Interest rate = 8%/4 = 2%

r = Semi annual Interest rate = (1+2%)^2 - 1 = 0.0404 = 4.04%

n = 2*2 = 4 semi annual payments

Debt Value = PV = $10,000

Semi annual payment = [r*PV] / [1 - (1+r)^-n]

= [4.04% * $10,000] / [1 - (1`+4.04%)^-4]

= $404 / 0.146509629

= $2,757.49784

Therefore, Semi annual payment is $2,757.50

Question b:

Amortization Schedule

Period	Opening Balance	Payment	Interest Portion	Principal Portion	Closing Balance
A	B	C	D = B*4.04%	E = C-D	F = B-E
1	10000	2757.5	404	2353.5	7646.5
2	7646.5	2757.5	308.9186	2448.581	5197.919
3	5197.919	2757.5	209.995911	2547.504	2650.415
4	2650.415	2757.5	107.0767	2650.423	0.0

Question c:

r = semi annual interest rate = 4.04%

n = 4 semi annual payments

x = 3 semi annual payments made

P = Semi annual payment = $2,757.50

Balance after 3 semi annual payments = P * [1 - (1+r)^-(n-x)] / r

= $2,757.5 * [1 - (1+4.04%)^-(4-3)] / 4.04%

= $2,757.5 * 0.038831219 / 0.0404

= $2,650.42292

Therefore, Balance after 3 payments is $2,650.42