Simple Questions

1. Simple Questions Practical uses of time value of money factors

2. Time Value Factors • TVM factors commonly used in determining equivalences • (F/P, i, N) • (P/F, i, N) • (F/A, i, N) • (A/F, i, N) • (P/A, i, N) • (A/P, i, N) • (P/G, i, N) • (A/G, i, N) • (P/A, g, i, N)

3. Simple Question • You are 20 yrs old and want to retire at age 60 with $1,000,000. How much do you have to put away each year if you earn 10% interest on it? • At age 5, you were left $10,000 from an aunt. Your parents put the money in a trust fund earning 10%/year. You are now 25 years old and may draw from the fund. How much money is there? • You buy a house for $100,000. You finance the full amount with a 30 years mortgage. The interest rate is 9%/yr and your payments are monthly. What is the total of all the payments made?

4. Simple Question (continued) • You can afford $300/month on a car. If the dealer’s interest rate is 6%/yr and the loan is for 60 months, how much can you finance? • You win the lottery and the government promises to pay $1,000,000 in ten years. Banks currently pay 10%/yr on savings. What is the prize worth to you right now? • You are a freshman in college and you just paid $1000 for tuition and fees for the University. Assuming the cost goes up by $100 per semester for the remaining 7 semesters of your education, how much do you have to have in the bank right now to cover the remaining charges? Assume your investments earn 3% every six months.

5. Simple Question (continued) • Your daughter starts college in 18 years. If you put $100/month in a CD returning 6%/year (compounded monthly), how much will you have then? • If $1000 is invested now, $1500 two years from now, and $800 four years from now at an interest rate of 8% compounded annually, what will be the total amount in 10 years? • What is the amount of 10 equal annual deposits that can provide for the following five annual withdrawals? The first withdrawal of $1000 is made at the end of year 11, and subsequent withdrawals increase at the rate of 6% per year over the previous year’s withdrawal. The interest rate is 8%, compounded annually.

6. Simple Question 1 • You are 20 yrs old and want to retire at age 60 with $1,000,000. How much do you have to put away each year if you earn 10% interest on it? • We want the value of equal payments that are equivalent to a future million of dollars. • The interest is compounded, and rate is 10%/yr • The number of periods is 40 years. • The answer comes from the equivalence between an future worth (F) and an annuity (A)

7. Simple Question 1 (cont’d) • N=40 years, • i=10%, • (A/F, i ,N) = i/((1+i)N –1) = 0.1/(1+0.1)40 –1) = 0.002259414 • Or alternatively, you can find that (A/F, i ,N) = 0.0023 at the end of the Workbook, on page 169 • F=$1,000,000 • Therefore, A = $1,000,000 (0.0023) = about $2,300.

8. Simple Question 2 • At age 5, you were left $10,000 from an aunt. Your parents put the money in a trust fund earning 10%/year. You are now 25 years old and may draw from the fund. How much money is there? • We want the future worth of an investment. • The interest is compounded, and rate is 10%/yr. • The number of periods is 20 years. • The answer comes from the equivalence between present worth (P) and future worth (F) • F = $10,000 (F/P,0.1 ,20) • 10,000 (6.7275) = $67,275

9. Simple Question 2 (cont’d) • N=20 years, • i=10%, • (F/P, i ,N) = (1+i)N = (1+0.1) 20 =6.7275 • Or alternatively, you can find that (F/P, i ,N) = 6.7275 at the end of the Workbook, on page 169 • P=$10,000 • Therefore, F = $10,000 (6.7275) = $67,275

10. Simple Question 3 • You buy a house for $100,000. You finance the full amount with a 30 years mortgage. The interest rate is 9%/yr and your payments are monthly. What is the total of all the payments made? • We want the present worth of the value of equal payments. • The interest is compounded, and rate is 0.75%/month. • The number of periods is 360 months. • The answer comes from the equivalence between an annuity (A) and a present worth (P).

11. Simple Question 3 (cont’d) • N = 360 months • i = 0.75% • (A/P, i, N) = (0.0075(1.0075) 360)/((1.0075)360 –1) = 0.0080462 • Therefore, A = P(A/P, i ,N) = 100,00 (0.0080462) = $804.62/month • Total of all payments = 360 (804.62) = $289,664.

12. Simple Question 4 • You can afford $300/month on a car. If the dealer’s interest rate is 6%/yr and the loan is for 60 months, how much can you finance? • We want the present worth of the value of equal payments. • The interest is compounded, and rate is 0.5%/mo. • The number of periods is 60 months. • The answer comes from the equivalence between an an annuity (A) and a present worth (P).

13. Simple Question 4 (cont’d) • N=60 months, • i=0.5%, • (P/A, 0.5, 60 )= 51.7256, • A = $300 • Therefore, P= $300 (51.7256) = $15,518

14. Simple Question 5 • You win the lottery and the government promises to pay $1,000,000 in ten years. Banks currently pay 10%/yr on savings. What is the prize worth to you right now? • We want the present worth of a future cash flow. • The interest is compounded, and rate is 10%/yr. • The number of periods is 10. • The answer comes from the equivalence between future worth (F) and present worth (P)

15. Simple Question 5 (cont’d) • N=10 years, • i=10%, • (P/F, i ,N) = 1/(1+i)N = (1+0.1) -10 =0.3855 • Or alternatively, you can find that (P/F, i ,N) = 0.3855 at the end of the Workbook, on page 169 • F=$1,000,000 • Therefore, P = $1,000,000 (0.3855) = $385,500.

16. Simple Question 7 • Your daughter starts college in 18 years. If you put $100/month in a CD returning 6%/year (compounded monthly), how much will you have then? • We want the future worth of a series of equal payments. • The interest is compounded, and rate is 0.5%/mo • The number of periods is 216 months. • The answer comes from the equivalence between an annuity (A) and future worth (F)

17. Simple Question 7 (cont’d) • N=216 months, • i=0.5%, • (F/A, i ,N) = ((1+i)N –1)/i = ((1+0.005) 216 -1)/0.005 = 387.3531944 • Unfortunately, your Workbook (page 161) can’t help here. • A=$100 • Therefore, F = $100 (387.3531944) = about $38,735.