Answer:
Step-by-step explanation:
From the first question:
We are to find PV of the annuity.
Using the formula:
Present value of Annuity = Annuity Amount × Present Value Annuity Factor i.e. PVAF (n , r)
Where , Annuity Amount = $4,000
n = No. of periods = 7 years × 4 quarters per year = 28 periods but since the first payment is at beginning of the quarter, Then, n = 27 when considered for PVAF
r = 6.2% / 4 quarters = 1.55%,
PVAF(n0,r) when first payment is at beginning of n i.e. n0 = 1 + { [1-(1+r)^ -n0 ]/r }
= 1 + { [1-(1+0.0155)^ {-27}]/0.0155 }
= 1 + [ (1 - 0.66015 ) ] / 0.0155]
= 1 + 21.926
= 22.926
PVAF(28,1.55%) = 22.926
Thus , Present Value of Annuity = $4,000 × 22.926 = $91704.00
2. Present value of Annuity due = Annuity Amount × Present Value Annuity Factor i.e. PVAF (n , r)
Present Value of Annuity = $90,000
n = No. of periods = 7.5 years × 4 quarters per year = 30 periods
r = 5.4% / 4 quarters = 1.35%,
PVAF(n,r) = [1-(1+r)^-n]/r
PVAF(n,r) = [1-(1+0.0135)^ -30]/0.0135
PVAF(30,1.35%) = (1 - 0.6688)/0.0135
PVAF(30,1.35%) = 0.3312/0.0135
PVAF(30,1.35%) = 24.53
Hence ;
$90,000 = Annuity Amount × 24.53
Annuity amount = $90,000/24.53 = $3,668.48
