Question

Suppose you receive $160 at the end of each year for the next three years.

a. If the interest rate is 8%​, what is the present value of these cash​ flows?

b. What is the future value in three years of the present value you computed in​(a​)?

c. Suppose you deposit the cash flows in a bank account that pays 8% interest per year. What is the balance in the account at the end of each of the next three years​(after your deposit is​ made)? How does the final bank balance compare with your answer in​(b​)?

Answer 1

a.

Year End	Amount Received	DF@8% (1/1.08^n)	Present value (Amount rec * DF)
1	$                     160.00	0.9259	$                    148.15
2	$                     160.00	0.8573	$                    137.17
3	$                     160.00	0.7938	$                    127.01
		TOTAL=	$                    412.34

b. The Future value will remain same as in Present value we have dicounted the amount with 8% and in future value we will compund it with 8% again which will nullify the effect.

So future vaue will be ($160 * 3 Years) = $$480

c. In this case we will compund the factors with 8%

	A	B	C
Year	Opening balance At start of year	Interest @8%	Amount Deposited @160 at end of year	Closing balance (A + B + C)
1	0	0	160	160
2	160	12.8	160	332.8
3	332.8	26.62	160	519.42

So the balance at the end of 3rd year = $519.42

The final bank balance differ between point b and C, as beacuse of the interest. In optiion B we have not shown the effect of interest earning, because of compunding and discounting. So the raw amount what we received is shown in B ($480), but in option C we have Amount + Interest ($480 + $39.42) i.e. $519.42.