Question

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?

Answer 1

Answer:

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