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Find the present values of these ordinary annuities. Discounting occurs once a year. Do not round...

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.

  1. $700 per year for 12 years at 8%.

    $   

  2. $350 per year for 6 years at 4%.

    $   

  3. $1,000 per year for 6 years at 0%.

    $   

  4. 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.  

Solutions

Expert Solution

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


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