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3 years ago

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A woman plans to work for 25 years and to make deposits into a retirement fund at the amount of 100 at the end of each month. Th

e fund earns 6% nominal, converted monthly. The fund will be used to purchase a 20-year annuity immediate at retirement, with the first payment in a month after retirement. Assuming the annuity is purchased at 5% nominal converted monthly, what is the amount of her monthly end-of-month payments during her retirement?

1 answer:

zaharov [31]3 years ago

8 0

Answer:

The answer is $457.35

Explanation:

FV= P * ([1 + I]^N - 1 )/I.

FV=100 * ([1 + 0.06/12]^(12*25 - 1 )/0.06/12=$69299.40

PV of an Annuity = C x [ (1 – (1+i)^-n) / i ]

$69299.40= C x [ (1 – (1+0.05/12^-12^*20) / 0.05/12 ]= <u>$457.35</u>

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Multiply 3.85% x $45,076 *

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I figured this out so the answer is 173542.6

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3 years ago

Assume (1) estimated fixed manufacturing overhead for the coming period of $221,000, (2) estimated variable manufacturing overhe

svetoff [14.1K]

Answer:

The predetermined plantwide overhead rate for the period is closest to:____.

$6.02

Explanation:

a) Data and Calculations:

Estimated fixed manufacturing overhead = $221,000

Estimated variable manufacturing overhead = $2.00 per DLH

Actual manufacturing overhead for the period = $320,000

Actual direct labor-hours worked = 54,000 hours

Estimated direct labor-hours to be worked in the coming period = 55,000 hours.

Predetermined plantwide overhead rate:

Estimated fixed manufacturing overhead = $221,000

Estimated variable manufacturing overhead = 110,000 ($2.00 * 55,000)

Total estimated manufacturing overhead = $331,000

Predetermined rate = $331,000/55,000 = $6.02 per DLH

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3 years ago

We observe the following annualized yields on four Treasury securities: (75%)

Anon25 [30]

Answer:

Explanation:

1.

From the given information;

The spot rate for maturity at 0.5 year $(X_1) = 4\%/2 = 2\%$

The spot rate for maturity at 1 year is:

= $\dfrac{22.5}{(1+X_1)}+ \dfrac{1000 + 22.5}{(1+X_2)^2}=1000$

= $\dfrac{22.5}{(1+0.02)}+ \dfrac{1000 + 22.5}{(1+X_2)^2}=1000$

= $\dfrac{22.5}{(1+0.02)}+ \dfrac{1022.5}{(1+X_2)^2}=1000$

By solving for $X_2$ ;

$X_2$ = 2.253%

The spot rate for maturity at 1.5 years is:

$= \dfrac{25}{(1+X_1)}+ \dfrac{25}{(1+X_2)^2}+ \dfrac{1000 + 25}{(1+X_3)^3}=1000$

Solving for $X_3$

$X_3$ = 2.510%

The spot rate for maturity at 2 years is:

$= \dfrac{27.5}{(1+X_1)}+ \dfrac{27.5}{(1+X_2)^2}+ \dfrac{27.5}{(1+X_3)^3} +\dfrac{1000+27.5}{(1+X_4)^4} =1000$

By solving for $X_4$ ;

$X_4$ = 2.770%

Recall that:

Coupon rate = yield to maturity for par bond.

Thus, the annual coupon rates are 4%, 4.5%, 5%, and 5.5% for 0.5, 1, 1.5, 2 years respectively.

2.

For n years, the price of n-bond is:

$= \dfrac{cash \ flow \ at \ year \ 1}{1+X_1}+ \dfrac{cash \ flow \ at \ year \ 2}{(1+X_2)^2}+... + \dfrac{cash \ flow \ at \ year \ b}{(1+X_n)^n}$

Thus, for 2 years bond implies 4 periods;

∴

$= \dfrac{40}{1+0.02}+ \dfrac{40}{(1+0.02253)^2} + \dfrac{40}{(1+0.0252)^3}+ \dfrac{40}{(1+0.0277)^4}$

= $1047.024

3.

Suppose there exist no-arbitrage, then the price is:

$= \dfrac{0}{(1+0.02)}+\dfrac{1000}{(1+0.02253)^2}$

= 956.4183

Since the market price < arbitrage price.

We then consider 0.5, 1-year bonds from the portfolio

Now;

weight 2 × 1000 + weight 2 × 22.5 = 1000

weight 2 × 1022.5 = 1000

weight 2 = 1022.5/1000

weight 2 = 0.976

weight 1 + weight 2 = 1

weight 1 = 1 - weight 2

weight 1 = 1 - 0.976

weight 1 = 0.022

The price of a 0.5-year bond will be:

$= \dfrac{1000}{(1+0.02\%)} \\ \\ =\mathbf{980.39}$

The price of a 1-year bond will be = 1000

Market value on the bond portfolio = 0.022 × price of 0.5 bond + 0.978 × price 1-year bond = 956.42

= 0.022 × 980.39 + 0.978 × 1000

= 956.42

So, to have arbitrage profit, the investor needs to purchase 1 unit of the 1-year zero-coupon bond as well as 0.022 units of the 0.5-year bond. Then sell 0.978 unit of the 1-year bond.

Then will he be able to have an arbitrage profit of $56.42

4.

The one-period ahead forward rates can be computed as follows:

Foward rate from 0 to 0.5 $X_1$ = 2%

Foward rate from 0.5 to 1

$(1+X_2)^2 = (1+X_1) \times (1+ Foward \ rate \ from \ 0.5 \ to \ 1 )$

$(1+0.0225)^2 = (1+0.02) \times (1+ Foward \ rate \ from \ 0.5 \ to \ 1 )$

Foward rate from 0.5 to 1 = 2.5%

Foward rate from 1 to 1.5

$(1+X_3)^3 = (1+X_2)^2 \times (1+ Foward \ rate \ from \ 1 \ to \ 1.5 )$

$(1+0.0251)^3 = (1+0.0225)^3 \times (1+ Foward \ rate \ from \ 1 \ to \ 1.5 )$

Foward rate from 1 to 1.5 =3.021%

Foward rate from 1.5 to 2

$(1+X_4)^4 = (1+X_3)^3 \times (1+ Foward \ rate \ from \ 1.5 \ to \ 2 )$

$(1+0.0277)^4 = (1+0.0251)^3 \times (1+ Foward \ rate \ from \ 1.5 \ to \ 2 )$

Foward rate from 1.5 to 2 =3.021%

5.

The expected price of the bond if the hypothesis hold :

= $\dfrac{40}{1+ 0.03021}+ \dfrac{1000+40}{(1+0.03285)^2}$

$= \dfrac{40}{(1.03021)}+ \dfrac{1040}{(1.03285)^2}}$

= 1013.724254

= 1013.72

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3 years ago

Jarrod receives a scholarship of $18,500 from Riggers University to be used to pursue a bachelor's degree. He spends $12,000 on

kodGreya [7K]

Answer:

Jarrod exclude from his gross income of $13,500

Explanation:

The following items which are excluded from the gross income are:

1. Tuition = $12,000

2. Books and supplies = $1,500

The total amount would be equal to

= $12,000 + $1,500

= $13,500

These items would be excluded because the deduction is allowed for these items. Whereas, the room and personal expenses are taxable. Hence, it would be included in the gross income

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nadya68 [22]

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4 years ago