Question

Loan of EGP 50,000 is taken out. A sinking fund is set up to pay back the EGP 50,000 in one lump sum at the end of 5 years. The sinking fund earns j2 = 12% and deposits are made semiannually. Find the book value of the debt after 2 years.

choose

3793.63

16595.67

33404.33

Answer 1

Payment required	=	FV*r /[(1+r)^n -1]
Future value	FV	50,000.00
Rate per period	r
Annual interest		12.0%
Number of payments per year		2
Interest rate per period		0.12/2=
Interest rate per period		6.000%
Number of periods	n
Number of years		5
Periods per year		2
number of periods		10
Period payment	=	50000*0.06/ [(1+0.06)^10 -1]
	=	3,793.40

Sinking fund payment is 3,793.40

FV of annuity	=	P * [ (1+r)^n -1 ]/ r
Periodic payment	P=	$                3,793.40
rate of interest per period	r=
Rate of interest per year		12.0000%
Payment frequency		Once in 6 months
Number of payments in a year		2.00
rate of interest per period		0.12*6/12	6.0000%
Number of periods
Number of years		2
Number of payments in a year		2
Total number of periods	n=	4
FV of annuity	=	3793.39791101919* [ (1+0.06)^4 -1]/0.06
FV of annuity	=	16,594.66
Loan amount		50,000.00
Less: sinking fund balance		-16,594.66
Loan book value		33,405.34

Answer is $33,405.33

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