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kondor19780726 [428]
3 years ago
5

Suppose that a 6.250% semi-annual coupon paying bond is priced at 105.500 per 100 of par value. The tenor of the bond is 13 year

s. What is the yield to maturity?

Business
1 answer:
zaharov [31]3 years ago
8 0

Answer:

5.70%

Explanation:

In this question, we applied the RATE formula that is shown on the attachment below:

Provided that,  

Present value = $1,000 × 105% = $1,050

Assuming figure - Future value or Face value = $1,000  

PMT = 1,000 × 6.250% ÷ 2 = $31.25

NPER = 13 years × 2 = 26 years

The formula is shown below:  

= Rate(NPER;PMT;-PV;FV;type)  

The present value come in negative  

So, after solving this, the yield to maturity is 5.70%

We assume the semi annual basis is followed so we half the interest rate and the coupon rate and doubles the time period

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2 years ago
1. Alex Meir recently won a lottery and has the option of receiving one of the following three prizes: (1) $74,000 cash immediat
sergey [27]

Answer:

1. The PV of option 3 which is $90,000 is the highest. Therefore, Alex will choose option 3 because it has the highset PV.

2. The fund balance after the last payment is made on December 31, 2027 will be approximately $1,934,302.71.

Explanation:

1. Assuming an interest rate of 6%, determine the present value for the above options. Which option should Alex choose?

Alex will choose the option with the highest present value (PV). The present value of each option can be determined as follows:

Option 1: $74,000 cash immediately

PV of option 1 = $74,000

Option 2: $26,000 cash immediately and a six-period annuity of $8,300 beginning one year from today

PV of $26,000 cash immediately = $26,000

PV of a six-period annuity of $8,300 beginning one year from today can be determined using the formula for calculating the present value of an ordinary annuity as follows:

PV of $8,300 annuity = P * ((1 - (1 / (1 + r))^n) / r) …………………………………. (1)

Where;

PV = Present value of the $8,300 annual payments today =?

P = Annual payment = $8,300

r = interest rate = 6% = 0.06

n = number of years = 6

Substitute the values into equation (1) to have:

PV of $8,300 annuity = $8,300 * ((1 - (1 / (1 + 0.06))^6) / 0.06)

PV of $8,300 annuity = $8,300 * 4.9173243260054

PV of $8,300 annuity = $40,813.79

Therefore,

PV of option 2 = PV of $26,000 cash immediately + PV of $8,300 annuity = $26,000 + $40,813.79 = $66,813.79

Option 3: a six-period annuity of $15,000 beginning one year from today

The PV of option 2 can be determined using the formula for calculating the present value of an ordinary annuity as follows:

PV of option 3 = P * ((1 - (1 / (1 + r))^n) / r) …………………………………. (2)

Where;

PV of option 3 = Present value of the $15,000 annual payments today =?

P = Annual payment = $15,000

r = interest rate = 6% = 0.06

n = number of years = 6

Substitute the values into equation (2) to have:

PV of option 3 = $15,000 * ((1 - (1 / (1 + 0.06))^6) / 0.06)

PV of option 3 = $15,000 * 4.9173243260054

PV of option 3 = $90,000

Based on the calculations, the PV of option 3 which is $90,000 is the highest. Therefore, Alex will choose option 3.

2. Assuming that the bank account pays 7% interest compounded annually, what will be the fund balance after the last payment is made on December 31, 2027?

This can be determined using the formula for calculating the Future Value (FV) of an Ordinary Annuity is used as follows:

FV = M * (((1 + r)^n - 1) / r) ................................. (3)

Where,

FV = Future value of the deposits after 10 years =?

M = Annual deposits = $140,000

r = annual interest rate = 7%, or 0.07

n = number of years = 10

Substituting the values into equation (3), we have:

FV = $140,000 * (((1 + 0.07)^10 - 1) / 0.07)

FV = $140,000 * 13.8164479612795

FV = $1,934,302.71

Therefore, the fund balance after the last payment is made on December 31, 2027 will be approximately $1,934,302.71.

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Answer:

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Explanation:

A budget is an estimate of the revenue and expenditure of a company over a specified period.

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