What is the present value of a fund that earns 15% on its balance each year, from which $10,000 must be paid a year for 6 years, after which the balance of the fund will be zero?

The present value of the fund=$25,939.66

Step-by-step explanation:

Step 1

Determine the future value of the fund as shown;

Future value (F. V) = payment amounts per year*number of years

where;

payment amounts per year=$10,000

number of years=6

replacing;

Future value (F. V) = (10,000*6) = 60,000

Future value (F. V) = $60,000

Step 2

Determine the present value (P. V) of the fund as shown;

F. V=P. V (1+r) ^n

where;

F. V=future value

P. V=present value

r=annual interest rate

n=number of years

In our case;

F. V=$60,000

P. V=unknown

r=15%=15/100=0.15

n=6

replacing;

60,000=P. V (1+0.15) ^6

60,000=P. V (1.15) ^6

P. V=60,000/{ (1.15) ^6}

P. V=25,939.66

The present value of the fund=$25,939.66