1. We have an investment of $15,000 on which we receive $1,000 yearly, as well a

Question

1. We have an investment of $15,000 on which we receive $1,000 yearly, as well as $20,000 7 years later. Compute the i on that investment.

2. We invest $10,000 for 10 years. We receive $14,000 10 years later. The i is 25% annually. What is the annual receipt we make?

The two problems have been solved already by another representative from Chegg, but my professor would like the class to use a formula for both problems. So, by looking at the work shown and the answers that Chegg came up with, is there a formula that can be used for both problems 1 & 2?

For answer 1, i is the interest rate, but are $15,000, $1,000, and $20,000 Present Value (PV) or Future Value (FV) or Annuity Payment (PMT)? Is 7 years n (number of years)? Also, is there a formula that you can provide that can help arrive at the answer i = 10.16%?

Answer 1.

Let interest rate be i%

Initial Investment is $15,000 on which $1,000 yearly for 7 years and $20,000 after 7 years.

Therefore, $15,000 = 1,000 / (1 + i) + 1,000 / (1 + i)2 + 1,000 / (1+i)3 + .. + 1,000 / (1 + i)7 + 20,000 / (1 + i)7 after 7 years

i = 10.16%

For Answer 2, is $10,000 the Present Value (PV)? Is 10 years n (number of years)? And is $14,000 Present Value (PV), Future Value (FV) or Annuity Payment (PMT)? Also, is there a formula that you can provide that can help arrive at the answer x = $2,379.71?

I would really appreciate your help because I need to answer these questions for an assignment. Thanks.

Answer 2.

Let X be the annual receipt.

Initial Investment is $10,000 and we will receive $14,000 after 10 years interest earned is 25%.

$10,000 = x / 1.25 + x / 1.252 + x / 1.253 + ... + x / 1.2510 + 14,000 / 1.2510

$8,496.76 = x / 0.25 x (1 - (1 / 1.25)10

x = $2,379.71

Explanation / Answer

Let X be the annual receipt.

Initial Investment is $10,000 and we will receive $14,000 after 10 years interest earned is 25%.

$10,000 = x / 1.25 + x / 1.252 + x / 1.253 + ... + x / 1.2510 + 14,000 / 1.2510

$8,496.76 = x / 0.25 x (1 - (1 / 1.25)10

x = $2,379.71

This is a simple problem based upon the present value of annuity.

Since the annual cash flow is not given, it is assumed to be x which will be received annually for next 10 years. Also, along with the annual receipt, an amount equivalent to $14,000 will be received at the end of 10 years. Now , we know the initial investment amount which is equal to $10,000. The rate of return is also provided i.e. 25 %, now we will set up an equation for the internal rate of return formula which states that IRR is the rate of return at which present value of cash outflow equals the present value of cash inflows. Present value of $10,000 which is the investment is $10,000. Now , the formula for IRR will look like:

CFW0=CFW1/ (1+r) + CFW2/ (1+r) ^2…………………..CFW n/ (1+r)^n

CFW0=Cash investment

CFW1,CFW2.......=Cash inflows

n =Number of years

10,000=x/ (1+.25) +x/ (1+.25)^2………………………………x/(1+.25)^10 + 14000/(1+.25)^10

X=2,379.71

In both the problems , an equation for IRR is set up which calculates a rate of return at which present value of cash outflow becomes equal to present value of cash inflows.

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