Question

In: Finance

What is the present value of a $100-payment, 100-year annuity due if the interest rate is...

What is the present value of a $100-payment, 100-year annuity due if the interest rate is 14% per year? What is the future value of a $50-payment, 50-year annuity due if the interest rate is 9% per year?

Expert Solution

a.

Present value of a $100-payment, 100-year annuity due

$ 814.28

Working:

a.

Present value of annuity due of 1

=

((1-(1+i)^-n)/i)*(1+i)

Where,

=

((1-(1+0.14)^-100)/0.14)*(1+0.14)

i

14%

=

8.14284054

n

100

b.

Present value of annuity

=

Annuity amount x Present value of annuity of 1

=

$ 100.00

x

8.142841

=

$ 814.28

b.

Future value of a $50-payment, 50-year annuity due

$ 44,422.05

Working:

a.

Future value of anuity due of 1

=

((((1+i)^n)-1)/i)*(1+i)

Where,

=

((((1+0.09)^50)-1)/0.09)*(1+0.09)

i

9%

=

888.441076

n

50

b.

Future value of annuity

=

Annuity amount x Future value of annuity of 1

=

$ 50.00

x

888.4411

=

$ 44,422.05

jeff jeffy answered 3 years ago

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