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.
