1. Practical uses of time value of money factors
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) =
Or alternatively, you can find that
(A/F, i ,N) = 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) = 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) =
Therefore, A = P(A/P, i ,N) = 100,00 ( ) = $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 )= ,
A = $300
Therefore, P= $300 ( ) = $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) = 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 =
(( ) )/0.005 =
Unfortunately, your Workbook (page 161) can’t help here.
A=$100
Therefore, F = $100 ( ) = about $38,735.