Question

You have your choice of two investment accounts. Investment A is a 12-year annuity that features end-of-month $3,400 payments and has an interest rate of 6 percent compounded monthly. Investment B is an annually compounded lump-sum investment with an interest rate of 7 percent, also good for 12 years.

How much money would you need to invest in B today for it to be worth as much as Investment A 12 years from now? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Present value: ?

Answer 1

Step-1:Calculate Future Value of Investment A

Future Value of Investment A

=

End of month payment x Future Value of Annuity of $ 1

=

$             3,400

x

210.1502

=

$ 7,14,510.55

Working:

Future Value of Annuity of $ 1

=

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

Where,

=

(((1+0.005)^144)-1)/0.005

i

6%/12

=

0.005

=

210.1501631

n

12*12

=

144

Step-2:Calculate Present Value of Above amount

Present Value

=

Future Value x Present Value of Future Value of $ 1

=

$       7,14,511

x

0.444

=

$ 3,17,251.23

Working:

Present value of $ 1

=

(1+i)^-n

Where,

=

(1+0.07)^-12

i

7%

=

0.444

n

12

Thus,

Required investment in B

=

$ 3,17,251.23