Answer:
This question is incomplete. Here’s what’s missing:
1. For transaction (a), calculate the present value of the debt.
2-a. For transaction (b), what amount must the company deposit on January 1?
2-b. What is the total interest revenue earned?
3. For transaction (c), find the present value of this obligation.
4-a. For transaction (d), how much will each equal annual payment on the note be?
4-b. What will be the total interest expense incurred?
Explanation:
a) A payment of $6,000 will be made at the end of each year for 7 years, and $115,000 will be paid at the end of the seventh 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) For the amount that will reach $490,000 with a 7% annual interest at the end of 8 years, let’s call it 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
Therefore, a deposit of $285,182 is necessary for 8 years at a 7% interest rate.
The total interest income 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 machinery's price is $170,000, with $34,000 paid upfront. The loan amount is ($170,000-$34,000)=$136,000.
The PVA factor at 7% annual compounding for 5 years is 4.1002.
Thus, the PMT = 136,000/4.1002
= $33,169.
This indicates that each yearly payment amounts to $33,169 for five years.
The total amount payable is ($34,000+$33,169*5)
=$34,000+$165845
=$199845.
The interest expense totals ($199845 - $170,000)
= $29,845.