Question

In: Finance

A.Calculate the present value of an annuity of $5,000 received annually that begins today and continues...

A.Calculate the present value of an annuity of $5,000 received annually that begins today and continues for 10 years, assuming a discount rate of 9%.

B. Joan invested $5,000 in an interest-bearing account earning an 8% annual rate of interest compounded monthly. How much will the account be worth at the end of 5 years, assuming all interest is reinvested at the 8% rate?

C. Calculate the present value of an ordinary annuity of $5,000 received annually for 10 years, assuming a discount rate of 9%.

D. Calculate the future value of $10,000 invested for 10 years, assuming an annual interest rate of 9%.

E. Calculate the present value of $10,000 to be received in exactly 10 years, assuming an annual interest rate of 9%

Solutions

Expert Solution

A. Present Value of Annuity $ 34,976.23
Working:
Present Value = Annuity x Present Value of annuity due of $ 1
= $   5,000.00 x              6.995
= $ 34,976.23
Present Value of annuity due of $ 1 = ((1-(1+i)^-n)/i)*(1+i) Where,
= ((1-(1+0.09)^-10)/0.09)*(1+0.09) i              0.09
=              6.995 n 10
B. Value of investment at the end of 5 years $ 7,464.04
Working:
Future Value = P*(1+i)^n Where,
= 5000*(1+0.0067)^60 i 8%/12 = 0.0067
= $   7,464.04 n 5*12 = 60
P = $        5,000
C. Present Value $ 32,088.29
Working:
Present Value of ordinary annuity = Annuity x Present Value of ordinary annuity of $ 1
= $   5,000.00 x              6.418
= $ 32,088.29
Present Value of ordinary annuity of $ 1 = (1-(1+i)^-n)/i Where,
= (1-(1+0.09)^-10)/0.09 i              0.09
=              6.418 n 10
D. Future Value $ 23,673.64
Working:
Future Value = P*(1+i)^n Where,
= 10000*(1+0.09)^10 P $       10,000
= $ 23,673.64 i                0.09
n 10
E. Present Value $   4,224.11
Working:
Present Value = F*(1+i)^-n Where,
= 10000*(1+0.09)^-10 F $       10,000
= $   4,224.11 i                0.09
n 10

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