Question

Gregor will receive $20,000 at the end of 6 years. If the interest rate is 7% per year, what is the present value of this cash flow?

A perpetuity will pay you $400 per year, forever. If the discount rate is 8%, what is this perpetuity worth today? 

Nicole will need $22,000 in nine years. She currently has $10,000 to invest. At what interest rate must she invest the money?  

Answer 1

Awnser 1 .

The formula for present value is:

PV = CF/(1+r)n

Where:
CF = cash flow in future period
r = the periodic rate of return or interest (also called the discount rate or the required rate of return)
n = number of periods

Let's look at an example. Assume that you would like to put money in an account today to make sure your child has enough money in 10 years to buy a car. If you would like to give your child $10,000 in 10 years, and you know you can get 5% interest per year from a savings account during that time, how much should you put in the account now? The present value formula tells us:

PV = $10,000/ (1 + .05)10 = $6,139.13

Thus, $6,139.13 will be worth $10,000 in 10 years if you can earn 5% each year. In other words, the present value of $10,000 in this scenario is $6,139.13.

It is important to note that the three most influential components of present value are time, expected rate of return, and the size of the future cash flow. To account for inflation in the calculation, investors should use the real interest rate (nominal interest rate - inflation rate). If given enough time, small changes in these components can have significant effects.

For calculation of present value the awnser is that

Present Value: 13,326.84

Total Interest: 6,673.16

2. Awnser

What Is Perpetuity?

A perpetuity is a security that pays for an infinite amount of time. In finance, perpetuity is a constant stream of identical cash flows with no end. The formula to calculate the present value of a perpetuity, or security with perpetual cash flows, is as follows:

Perpetuity Example

For example, if a company is projected to make $100,000 in year 10, and the company’s cost of capital is 8%, with a long-term growth rate of 3%, the value of the perpetuity is as follows:

=r−gCash FlowYear 10​×(1+g)​=0.08−0.03$100,000×1.03​=0.05$103,000​=$2.06 million​

Awnser of problem :- 5000

3 awnser :-

If we invest 10000 for 9 year and we want interest 22000 then we need atleast 13.5% interest rate