Question

How much must be invested today in order to generate a 5-year annuity of $1,000 per year, with the first payment 1 year from today, at an interest rate of 12%?

Answer 1

Answer:

The amount to be invested today is $3604.78

Explanation:

This is a case of an ordinary annuity,to calculate the present value, the below formula is made used of:

PV=A*(1-1/(1+r)^N)/r

A is the annuity payment of $1000 for 5 years

r is the rate of return on the annuity of 12%

N is the duration of the annuity payment , that is 5years

PV=$1000*(1-1/(1+12%)^5)/12%

PV=$3604.78

In essence, in order to receive $1000 every year starting a year today for 5 years, the sum of $3604.78 must be deposited today at rate of return of 12% per year.

The amount required would be been different if the first payment of $1000 is due today