Question

Suppose your client wishes to purchase an annuity that pays $110,000 each year for 8 years, with the first payment 5 years from now. At an interest rate of 5%, how much would the client need to invest now

Answer 1

Initial investment= $557,050.6

Step-by-step explanation:

Giving the following information:

Annual payment= $110,000

Interest rate= 5%

Number of payments= 8

First, we need to determine the value of the annuity five years from now. We will use the following formula:

PV= A*{(1/i) - 1/[i*(1 + i)^n]}

A= annual payment

PV= 110,000*{(1/0.05) - 1/[0.05*(1.05^8)]}

PV= $710,953.40

Now, the initial investment now:

PV= FV / (1 + i)^n

PV= 710,953.4 / (1.05^5)

PV= $557,050.6