Question

4. Find the present values of these ordinary annuities. Discounting occurs once a year.

(a) $400 per year for 10 years at 10%

(b) $200 per year for 5 years at 5 %

(c) $400 per year for 5 years at 0%

(d) Rework parts a, b, and c assuming they are annuities due.

Please give me the process, thank you!

Answer 1

a) An annuity is an insurance contact that promise to pay regular income either immediately or iin the future .

SOLUTION

PMT=$400

I=10%

N=10 Years

FV= PMT*(1+i) ^ n-1/i (1+i) ^ n-1/i

FV = $400 * (1+0.10)^ 10-1/0.10 (1+0.10)^ 10-1/0.10

FV =$400*15.9374 = $6,374.96

b) PMT = $200, I=5%, N=5 Years

FV = PMT*(1+i)^ n-1/i (1+i)^ n-1/i

FV = $200*(1+0.05)^5-1/0.05(1+0.05)^5-1/0.05

FV = $200*5.5256

FV=1,105.12

c) PMT =$400

I = 0%

N=5 Years

FV = PMT*N

FV =$ 400*5

FV=$2,000

d) Rework parts a , b & c assuming they are annuities due

a) PMT=$400, I=10% N=10 years

FV=$400*(1+0.10)^10-1/0.10(1+0.10)^10-1/0.10*1.10

FV = $400*15.9374*1.10

FV =$ 7,012.46

b) PMT=$200,I=5%,N=5 years

FV = $200*(1+0.05)^5-1/0.05(1+0.05)^5-1/0.05*1.05 (1+i)

FV =$200*5.5256*1.05

FV =&1,160.38

c) PMT =$400, I=0%,N=5years

FV =PMT*n*(1+i )

FV = $400*5*1

FV=$2000

Present value of annuities of those ordinary annuities discounting occurs once a year

a) PMT=$400,I=10%, N=10

PV = PMT*(1+i)^n-1/i*(1+i)^n(1+i)^1/i*(1+i)^n

PV = $400*(1+1.10)^10-1/0.10*(1+0.10)^10(1+0.10)^1/0.10*(1+0.10)^10

PV =$400*6.1446

PV=$2,457.83

b) PMT =200,I=5%,N=5

PV=$200*(1+0.05)^5-1/0.05*(1+0.05)^5(1+0.05)^5-1/0.05*(1+0.05)^5

PV =$200*4.3295

PV=$865.90

c)PMT=400,I=0%,N=5

PV =$400*5

PV=$2000