Answer:
a) A sum of $6,000 is to be paid at the end of each year for 7 years and the principal amount $115,000 to be paid at the end of 7th year.
PV=$6,000/(1+0.07)^1 + $6,000/(1+0.07)^2 +$6,000/(1+0.07)^3 +$6,000/(1+0.07)^4 +$6,000/(1+0.07)^5 +$6,000/(1+0.07)^6 +$6,000/(1+0.07)^7 +$115,000/(1+0.07)^7
PV=$5,607.47 + $5,240.63 + $4,897.78 + $4,577.37 + $4,277.91 + $3,998.05 + $3,736.49 + $71,616.22
PV=$103,951.92
b) Let the single sum that will grow to $490,000 at 7% interest per annum at the end of 8 years be X
FV=PV(1+i)^n
$490,000 = X(1+0.07)^8
Thus,
X= $490,000/(1.07)^8
X = $490,000/1.7182
X = $285,182
Thhus, a single sum of $285,182 needs to be deposited for 8 years at 7% interest p.a.
The total amount of interest revenue is ($490,000-$285,182) = $204,818
c) PV = $75,000/(1.07)^1 + $112,500/(1.07)^2 + 150,000/(1.07)^3
PV = $70,093.45 + $98,261.85 + $122,444.68
= $290,800
FV =$75,000*(1.07)^1 + $112,500*(1.07)^2 + 150,000*(1.07)^3
= $80,250 + $85,867 + $91,878
= $257,995
d) The cost of the machine is $170,000. Immediate cash paid $34,000. Loan Amount is ($170,000-$34,000)=$136,000
The PVA factor at 7% p.a compounded annually for 5 years is 4.1002
Thus, the PMT = 136,000/4.1002
= $33,169
Thus, the amount of each annual payment is $33,169 for 5 years.
The total amount to be paid is ($34,000+$33,169*5)
=$34,000+$165845
=$199845
The interest expense is ($199845 - $170,000)
= $29,845
