Question

A bank in Toronto issued bonds for $750,000 that were redeemable in eight years. It established a sinking fund that was earning 4.50% compounded semi-annually to retire this debt on maturity and made equal deposits at the beginning of every six months into the fund.

a. Calculate the size of the periodic deposits.

Round up to the next cent

b. Calculate the fund balance at the end of the 8^th payment period.

Round to the nearest cent

c. Calculate the interest earned in the 9^th payment period.

Round to the nearest cent.

d. Calculate the amount by which the sinking fund increased in the 9^th payment period.

Round to the nearest cent.

e. Construct a partial sinking fund schedule to illustrate details of the first two payments.

Payment Period	Payment	Interest Earned	Increase in the Fund	Fund Balance	Book Value
0				$0.00	$750,000.00
1
2

Answer 1

a.

amount to be deposited at the beginning of every 6 months so that the amount deposited along with the [email protected]%PA, compounded semiannually would sum $750000 at the end of 8th year.

Where FVA = Future value of the annulty deposite= $750000

r= Rate of interest per period = 4.5%/2 = 2.25%

n= Number of Compounding period = 8 years*2= 16

=> A = $38594

Hence the size of periodic deposite is $38594 per beginning of each six months

	start principal	start balance	[email protected]% on start balance	end balance	end principal
1	$38,594.00	$38,594.00	$868.36	$39,462.37	$38,594.00
2	$77,188.00	$78,056.37	$1,756.29	$79,812.63	$77,188.00
3	$115,782.00	$118,406.63	$2,664.14	$121,070.78	$115,782.00
4	$154,376.00	$159,664.78	$3,592.45	$163,257.24	$154,376.00
5	$192,970.00	$201,851.24	$4,541.64	$206,392.89	$192,970.00
6	$231,564.00	$244,986.89	$5,512.22	$250,499.10	$231,564.00
7	$270,158.00	$289,093.10	$6,504.59	$295,597.69	$270,158.00
8	$308,752.00	$334,191.69	$7,519.33	$341,711.01	$308,752.00
9	$347,346.00	$380,305.01	$8,556.86	$388,861.87	$347,346.00
10	$385,940.00	$427,455.87	$9,617.77	$437,073.63	$385,940.00
11	$424,534.00	$475,667.63	$10,702.52	$486,370.15	$424,534.00
12	$463,128.00	$524,964.15	$11,811.70	$536,775.84	$463,128.00
13	$501,722.00	$575,369.84	$12,945.83	$588,315.66	$501,722.00
14	$540,316.00	$626,909.66	$14,105.47	$641,015.13	$540,316.00
15	$578,910.00	$679,609.13	$15,291.20	$694,900.33	$578,910.00
16	$617,504.00	$733,494.33	$16,503.62	$749,997.96 = $750000	$617,504.00

-----------------------

b. Fund Balance at the end of 8th payment = $341,711.01

c. Interest earned in the 9 th payment period = $8,556.86

d. sinking fund in 9th payment period has increased = Payment in 9 th Period + Interest Earned = $38594+ $8556.86 =$47150.86 or $47151(round off)

e.

Payment Period	Payment	interest [email protected]%	Increase in fund(Paymnet + Interest)	end Fund Balance
0	0	0	0	$0
1	$38,594.00	$868.36	$39,462.37	$39462.37
2	$38594.00	$1,756.29	$40350.29	$79812.63