Question

Blackwell, Inc. has a $125,000 liability it must pay five years from today. The company is opening a savings account so that the entire amount will be available when this debt needs to be paid. The plan is to make an initial deposit today and then deposit an additional $30,000 each year for the next three years, starting one year from today. The account pays a 5 percent rate of return. How much does the firm need to deposit today

Answer 1

Initial investment= $23,838.78

Step-by-step explanation:

Giving the following information:

Future Value (FV)= $125,000

Number of periods (n)= 5

Interest rate (i)= 5%

First, we need to calculate the future value of the three deposits using the following formula:

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

A= annual deposit

FV= {30,000*[(1.05^3) - 1]} / 0.05

FV= $94,575

Difference= 125,000 - 94,575= $30,425

Now, the initial investment today:

FV= PV*(1 + i)^n

Isolating PV:

PV= FV / (1 + i)^n

PV= 30,425 / (1.05^5)

PV= $23,838.78