First national bank

a) Draw time lines for
a $100 lump sum cash flow at the end of the year
an ordinary annuity of $10º per year for 3 years
an uneven cash flow stream of $50, $100, $75, and $50 at the end of the years 0 through 3 year if it is invested in a account paying 10 percent, annual compounding?

LUMP-SUM AMOUNT: a single flow, a $100 inflow in Year 2:

0 1 2 3 Year

100Cash flow

ANNUITY: a series of equal cash flows occurring over equal intervals:

0 1 2 3 Year

100 100 100 Cash flow

UNEVEN CASH FLOW STREAM: an irregular series of cash flows that do not constitute an annuity:

0 1 2 3 Year

-50 100 75 50 Cash flow

b) What is the future value of an initial $100 after 3 years if is invested in an account paying10 percent, annual compounding?
= 133.1
What is the present value of $100 to be received in 3 years if the appropriate interest rate is 10 percent, annual compounding?
= 75.13

c) We sometimes need to fin how long it will take a sum of money to grow to some specified amount. For example, if a company sales are growing at a rate of 20 percent per year how long will it take sale todouble?
= 3.8 años

d) What is the difference between an ordinary annuity and an annuity due?
Ordinary annuity / Vencida: Es cúando los pagos se realizan al final del mes.
Annuity due/ Anticipa: Es cuando los pagos de la anualidad se dan al principio.

What type of annuity is shown below? How would you change it to the other type?

0 12 3

100 100 100
Esta es una anualiudad vencida

1 2 3

100 100 100

Esta es una anualidad anticipada

e) What is the future value of a 3 year ordinary annuity of $100 I f the appropriate interestrate is 10% annual compounding?

What is the present value of the annuity? (3) What would the future and present values be if the annuity were an annuity due?

f) What is the present value of the following uneven cash flow stream? The appropriate interest rate is 10% compound annually.

g) What interest rate will cause $100 to grow to $125.97 in 3 years stream?

h) Willthe future value be larger or smaller of we compound an initial amount more often than annually, for example every 6 months, or semiannually, holding the stated interest rate constant? Why?
Mayor porque se capitalizan más veces el capital y los intereses.
Define (a) the stated, or quoted, or nominal, rate (b) the periodic rate, and (c) the effective annual rate (EAR)
Tasa nominal: la demercado, se exhibe y normalmente son anuales.
Tasa periódica: el número de periodos también es nominal.
Tasa efectiva: para poder comparar las tasas periódicas.
What is the effective annual rate corresponding to a nominal rate of 10%, compounded semiannually? Compounded quarterly? Compounded Daily?
(1+.10/2)²-1= 0.1025
(1+.10/4)⁴-1= 0.1038
(1+.10/360)³⁶⁰-1= 0.1052
What is the FV of$100 after 3 years under 10% semiannual compounding? quarterly compounding?
FV= 100(1+.10/2)⁶=134.009
FV= 100(1+.10/4)¹²=134.489
i) When will the effective annual rate be equal to the nominal (quoted) rate?
Cuando son anuales.
j) 1) What is the value at the end of year 3 of the following cash flow stream if the quoted interest rate is 10 percent, compounded semiannually?(1+.10/2)²-1=10.25%
FV= 100/.1025((1+.1025)³-1)=331.80
2) What is the PV of the same stream?
PV= 100/.1025(1-1/(1.1025)³)=247.59
3) Is the stream an annuity?
Sí, es una anualidad.
4) An important rule is that you should never show nominal rate on a time line or use it in calculations unless what condition holds? (hint Think of annual compounding, when ) What would be wrong with your answer to...