Using a Timeline to Solve Time Value of Money Problems

Check your understanding

5 questions

1. 1. When drawing a timeline for a loan repayment problem, which direction do cash flows typically move to represent money received versus money paid out?
   Both inflows and outflows point in the same direction by conventionInflows (money received) are shown as positive (upward arrows) and outflows (money paid) are shown as negative (downward arrows)Inflows are shown as negative and outflows as positive, since borrowing creates a liabilityTimelines only show the magnitude of cash flows, not their direction
2. 2. In the loan example ($10,000 at 12% annual interest, 2-year term with monthly payments), what is the correct value of N to enter into the financial calculator?
   21224120
3. 3. Using the loan example ($10,000 at 12% annual rate, monthly payments for 2 years), what monthly payment (PMT) does the calculator return, and which calculator setting is critical to getting this result?
   PMT ≈ $500.00; setting N = 24PMT ≈ $461.45; setting I/Y = 1 (monthly rate entered directly)PMT ≈ $588.92; setting P/Y = 2 for semi-annual compoundingPMT ≈ $470.74; setting P/Y = 12 so the calculator converts the annual rate to a monthly rate
4. 4. On a loan repayment timeline, where is the present value (PV) of the loan located?
   At the final payment period (end of the timeline)Midway along the timeline, representing the average cash flowAt time 0 (the beginning of the timeline), representing the lump sum received todayAt time 1, since interest begins accruing after the first period
5. 5. A borrower takes a $15,000 loan at a 9% annual interest rate to be repaid with monthly payments over 3 years. Which set of calculator inputs is completely correct?
   P/Y = 1, N = 3, I/Y = 0.75, PV = 15,000P/Y = 12, N = 3, I/Y = 9, PV = 15,000P/Y = 12, N = 36, I/Y = 9, PV = 15,000P/Y = 12, N = 36, I/Y = 0.75, PV = 15,000