In: Finance
Find the present values of these ordinary annuities. Discounting occurs once a year. Do not round intermediate calculations. Round your answers to the nearest cent.
$700 per year for 12 years at 8%.
$
$350 per year for 6 years at 4%.
$
$1,000 per year for 6 years at 0%.
$
Rework previous parts assuming they are annuities due.
Present value of $700 per year for 12 years at 8%: $
Present value of $350 per year for 6 years at 4%: $
Present value of $1,000 per year for 6 years at 0%: $
Please, if possible, can you explain how to find the answers on the BAII Plus Calculator. Thanks in advance.
Ordinary annuity:
A.
Annuity (P) = 700
number of years (n) =12
interest rate (i) =8%
Present value of ordinary annuity formula = P*(1-(1/(1+i)^n))/i
=700*(1-(1/(1+8%)^12))/8%
=5275.254612
Present value of this annuity is 5275.25
Financial calculator steps for ordinar annuity
rate = 8%
n = 12
PMT = -700
year end or beginning = 0
Press CPT and PV, result is 5275.25
b.
Annuity (P) = 350
number of years (n) =6
interest rate (i) =4%
Present value of ordinary annuity formula = P*(1-(1/(1+i)^n))/i
=350*(1-(1/(1+4%)^6))/4%
=1834.7479
Present value of this annuity is 1834.75
c
Annuity (P) = 1000
number of years (n) =6
interest rate (i) =0%
Present value of ordinary annuity formula will become inapplicable as denominator i is 0%
But as interest rate is 0%, PV = Number of annuity * annuity amount
=1000*6
=6000
Present value of this annuity is 6000
Annuity due:
A.
Annuity (P) = 700
number of years (n) =12
interest rate (i) =8%
Present value of annuity due formula = P+(P*(1-(1/(1+i)^(n-1)))/i)
=700 + (700*(1-(1/(1+8%)^(12-1)))/8%)
=5697.274981
Present value of this annuity is 5697.27
Financial calculator steps for ordinar annuity
rate = 8%
n = 12
PMT = -700
year end or beginning = 1
Press CPT and PV, result is 5697.27d
b.
Annuity (P) = 350
number of years (n) =6
interest rate (i) =4%
Present value of annuity due formula = P+(P*(1-(1/(1+i)^(n-1)))/i)
=350+(350*(1-(1/(1+4%)^(6-1)))/4%)
=1908.137816
Present value of this annuity is 1908.1
c
Annuity (P) = 1000
number of years (n) =6
interest rate (i) =0%
Present value of annuity due formula will become inapplicable as denominator i is 0%
But as interest rate is 0%, PV = Number of annuity * annuity amount
=1000*6
=6000
Present value of this annuity is 6000