UNIT 4 Exam Review: Annuities

Short Answer Type Questions

R[ (1 + iY' - 1]A=-----

1. Use the formula Calculate A for R = $500, i= 0.06, and n = 14.

2. Determine the amount of an ordinary simple annui of $1500 deposited each month for 4 years at 6.1% per yearcompounded monthly. ~~ PI ::0 R . 1+ lJ 1'\- I

3. Jordan wants to save $10 000 for a vacation. He deposi~ $150 at the end of each month for 4.5 years in an account thatearns 8.7% per year compounded monthly. Will Jordan have enough money saved at the end of 4.5 years? Why?

4. For 7 years, Sheri deposits $3350 at the end of each year into an account that earns 19.7% per year compounded annually.Determine the interest earned.

5. Jarret and Emma are saving for retirement. Jarret invests $700 at the end of each quarter for 30 years.Emma starts 15 years later and invests $1400 at the end of each quarter for 15 years. Assume each annuity earns 2% peryear compounded quarterly. Who will have more money saved for retirement? Why?

R[ 1 - (1 + i)-.'I ]PV=-----

6. Use the formula Calculate the value of PVfor R = 775, i= 0.028, and n = 34.

7. Mina is selling her business. The buyer offers her a choice:She can receive a payment of$7500 each month for 6 years, or she can receive a single cash payment of$350000immediately.Assume that money can be invested at 11.8% per year compounded monthly. Which payment should Mina accept? Explainyour reasoning.

8. Finn wants to save $75 000 over 3 years. He plans to make equal quarterly deposits in an account earning 5.4% per yearcompounded quarterly. What is Finn's quarterly deposit?

Problem Type Questions9. Kristina wants to save $10 000 for a vacation. She deposits $200 at the end of each month in an account that earns 7.9% per

year compounded monthly, (Hint: Use Future Value)a) What is the amount in the account after 3.5 years?b) How much interest is earned?c) Will Kristina have enough money saved at the end of3.5 years?

10. Frank plans to pay back a loan of $230 000 in 5 years. He makes quarterly payments at the end of each quarter.The bank charges 7.8% per year compounded quarterly. (hint: use Present Value)a) Determine Frank's quarterly payment.b) Does Frank's payment double under each change? Justify your answers.

i) The amount is twice as great, $460 000.ii) The interest rate is twice as great, 15.6%.iii) The time period is twice as long, 20 years.

11. Laurie and Jess both plan to save $220 000 over 6 years. Laurie saves by making regular monthly deposits in a GIC thatearns 6.7% per year compounded monthly. Jess saves by making regular monthly deposits in a high-performance mutualfund that earns 8% per year compounded monthly. (Use Future Value)a) Determine the monthly deposit for each savings plan.b) How much extra interest does Jess earn? Justify your answer.

IV

~!.~h = rza I -f- c)"- IJ

(, L '14' J~ 5.00L( I +V.(9c,) - \_

0.0('-::::5DO CO.;2 G-- rJ

0.010

~ $Ot> (\. Llo).-::.--

0.00

L~\DSD1.~

l-=- 0.0 (p

V\ -z: fL(- .

~J _ f1--;:?!Z::::~150oh -::::Lf'lC ld -::::tfq

L.:: 0, oc- J IJ\ D S 0::::-c.;, 0 06/;;-

Pt:;;:: ISDD ITI + 0, OOSce.) If-f_ (JO.OOfOg

-

- 15DO[I ,.1.1 (,-IJo .DOSOg

-::::P;Ol? (0,';).7ro)D.OOS'o8

Jl-3. K-==1150

h::: L·U; Y-- !.2 :::::-54-G-:::Q .08, ::: 0, OOIJ.~

ld-

O.OO/;;2S

_ 11,,51o ,001 d.-~

~ t~~~_~.~SJ",0•• ~.~ uJD1" 't ~ ~Iv~. t\-L- J.~ M~

~l~8.1S; ~J--

~l- d~~vw UJy\rUJ~~

R;::$3350Y):::: l,>, 1==7

L:: o,\I:n.:: O,\cn-t

- -A = 33t)D (6+- 0, lql)/ -IL6l,l(n

~ 23So( 6Z ,c)d.-J

o llcn

I ::::A-RV)

:= 4;1~log,~H -(3 $50)("1)

l~~ 0 ~ aLtA~ud (104-{t.6'4-

~_:~--Q,v~ .

*5, -JG\.rreJ--~ rz Jt 100

Y\.:::- 3D Xi tf.=: l~o

L ::=: O,O~ =- DlD05

i-f

l.,\20 l

A~ 100 [0 +0,(06) -~

0.00)

::: 100 (0 .~\t1)

OlOOS

== $, I tf 1\S.. 5+

~ YYWY\. &A ~ R= t 1 LfCo()-;::: t5xL(-.:::(OO

L ~ 0,005

A=- (R [O+l)" ~ 11L

ho Il::=: Pt-aD C( \ + D. CVC;) -

O..DO:;

- ILtoO (0. 3Lf-C1)D,ooS

= $ Cll blg.OL(

L

P V,=- -77 5 [ i - ( 1+O,6;)J~)5~

o ,Od. 'is'=-- 171) (\ - e.:set I~

o ,Od.-g

-=- lIS (0 .00&q)o cO;:),,&'

pv== fR==-l7~f\= 34-L::: O.O:2!? .

:,~~~~ CLU£ff-

optWn CD PClY~tD~ tl£;oO D.-Movl'f1A

+all lo~eO-~) b~LSe'I -\- (S YY)0 t:~ r(\ o- e...y

~~\A- +tv UA-S t,p(}..y~ .

-1ft, R~ '?{\~l~OOOY\-= '5)(.. 4-::: (;;:L

'l;::::-O. 0'5L{' - o. 0 /3 t;--y

A;fZ:::- v

lCi +~y\-7Jr<. == (J50oo)(o,O{5~)

C(I+O,OI3S) 12 _/ JfZ-=:- fDl"J.)

o,IlLf-G:,

R =- i rJ, ctCf . if I vb hI)' n s 9uaJi-erCCj d-0~?

~. WtLV\.D- t 10 ( 000 .

IX. \ tt-f+.eI '3,)" ~ e.O<VS ~ A:::?') R -::-.;tbO

VI-:=- 35',<.l~~t+;;Z

L ~ 0, 0,0 z: D. DO b~ ~l~

b)r= i1-(Plh)=~b'3q.lc) ~ (;200)(~)

~ 0JCoYl,l<1 - ~4ool--~=-----fi~"'§ _~----------------~--------::- 0 -fV

~\Q .~) Lo{,\.V\~'P 01-30 0 0 -\2..:::. ?(\ z: 5)L 4-~ ~D

'G~ ~g -z: D(OI~SLf

--------_._-_. ----

o-= ;)00 [(1+O.oo~s~f~/J _

o ,oo~:S~

~ d- 00 (D."5 \ -, /"3 ')

o,OO£oS&

\ =::- it c) ro3Cj .l Cj ] ~t-ev j. s;-L1~CLX~~

R::: p.\! C ~ \ _

G- (I + GfV\]

_ 1230000 (0. OlCl\l

CI - (l,otq~)-d-<:J

:::c '14~SD. o3~o4-'

~~ \3qC1~.d-1 vlI).,/ ·irram..-/i.? q u.a.x f-if~

PCLli~+ ' ~

-ftIO.b) CI\ PV~lfboOOO

r-::: ?R::.. PU(LJ

C\-{U+'lrh~fZ:: 4louDOO (o.O{~s-) .

[1- C\.O\4~r2~JR::: 'Z no

o.3;;(oL/'

K= $..;:)..1ctq~,'S'3

(It) PVcd50000

~::::?VI::: d-D

v= ~(,;..::. 0,03'1 .tt

0°0 ~/ \,u~ ~~ p~

VoJ.,w. uA :l)C. L:Ul 11'" e.cJ-/

--}It P~j (h£rJ-:s Q/L.e d Ou,/::J~ r

--------------

R:: PVCG)G - U+0TV\]

=- (~3 DODO) (D.O~q)

(\_ (\.O~q)-20J

- 8C1100.531.\1

o~ 0 no) -r& p CM1m.hYVf1-

~ rwt cto~ r o-rJ;iUig U0 Cfi.P.Rdt0 .

.---.- ..-----~-.-- -----------------

(\'(\) p v z: d 30000K-:::J

Yl -;:: dO ~ Lf z; gb

l= O. \)l~ z: D,OlqS-.V\.

R== Pv (~)0- ('+~Tr\J

=- J..30000(O,Olqs-)

Q - (I.D\ll S'r~J- 'tl.{--g 5

Dr7~bl- $S7ol.lif- .&Q 1[0; ~~ ": .

f.vtLlj~ 1J'6 «, LOwYl ~ r>

dLMeB<U. '-I~ FCU;rn.Q!I~' ~

'-

-:fr l L ~l~ri e. : It::: ~ 0 000h z: b ~ la:::- I d-.

G =- 0, O~7 ~ 0, O()5S~)::J-

Jes s : 1f:=:.;)R- 0000

h = fa \(. I~ :;::.7(;)..,L:::- 0, of

~ :::.0,000+ ,

rz~ A-c _([I+~)"-/J

::: (~~O cOO)(P, 00 r;;; <) c;g). 7:) ]C U+o,cd5g) - I

-z: /;):11, ~O. l/-9d-.\(

----rz - tJJfCt/./5

R~ A-~(O+L)Y)-/J

z: (Q(2DoOO)(D10007)

C{J + Of OGb7l,x-/]

= /L{-7'/-

~. 6/ Pf--R ~__,%' ~·3~-7~t,I j

--_._---'

b) Llu,ri e .:r~1\ rf~ffi\rn A .h

v:VlJV~IYt'U \f\.-'·O'ttLl Dep os if; P'+Cf. {. (S ) (7;J.) ~ t /7'1 3fc~ ~()I .

J-e..sS"loW D,eposd ; (,;u&'7. [,1) hd)--t 17/ /~ 07. '1~

[;\ClYR I"+eces t ~ I{: I 7'1 g W. 8'D -I{;17 I ') 07 ,cp =~'~S~