Question

Suppose you receive ​$130 at the end of each year for the next three years. a. If the interest rate is 10 %​, 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 10 % 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

Step-by-step explanation:

a. Present value formula:

PV= FV /(1+i)^n

FV: future value

i: interest rate

n: number of periods

-year 1: $130 to year 0 or to present value (PV):

PV=$130/(1+10%)^1

PV=$118.18

-year 2: $130 to year 0 or to present value (PV):

PV=$130/(1+10%)^2

PV=$107.43

-year 3: $130 to year 0 or to present value (PV):

PV=$130/(1+10%)^3

PV=$97.67

The sum of the three cash inflows: $118.18+$107.43+$97.67=$323.28

b. The future valur formula is:

VF=VP(1+i)^n

The future value of $323.28

VF= $323.28(1+10%)^3

VF= $430.28

c. Compound interest formula:

Final Capital (FC)= Initial Capital (IC)*[(1+interest(i))]^(number of periods(n))

-Year 2(because at the end of year 1 you received the first $130):

FC= $130*(1+10%)^1

FC=$143

At the end of Year 2: $143+$130=$273

-Year 3

FC= $273*(1+10%)^1

FC= $300.30

At the end of Year 3: $300.30+$130= $430.30

The final bank balance is the same as the answer in (b) because the compound interest formula that banks use is the same as the future value formula of cash flows.