Question

Question 1:

A) Assume that you will deposit $4000 at the end of each of the next three years in a St. George bank account paying 8% interest. You currently have $7000 in the account. How much will you have in three years? In four years?

B) You are looking into an investment that will pay you $12,000 per year for the next 10 years. If you require a 15% return, what is the most you would pay for this investment?

C) A bond has an 8% coupon, paid semi-annually. The face value is $100, and the bond matures in 6 years. If the bond currently sells for $91.137, what is the yield to maturity? What is the effective annual yield?

I need proper calculation with justification whereas required.

Answer 1

A.Information provided:

Present value= $7,000

Yearly deposit= $4,000

Interest year= 8%

Time= 3 years

The question is solved in two parts. First, the value of the $7,000 after 3 years needs to be computed.

Enter the below in a financial calculator to compute the future value:

PV= -7,000

N= 3

I/Y= 8

Press the CPT key and FV to compute the future value.

The value obtained is 8,817.98.

The value of the $7,000 after 3 years is $8,817.98.

Next, the value of the yearly deposit of $4,000 needs to be computed.

Enter the below in a financial calculator to compute the future value of the yearly deposit:

PMT= $4,000

N= 3

I/Y= 8

The value obtained is 12,985.60

The value of the value of the yearly deposit of $4,000 is $12,985.60

Therefore, I will have $8,817.98 + $12,985.60= $21,803.58 after 3 years.

b. Information provided:

Present value= $7,000

Yearly deposit= $4,000

Interest year= 8%

Time= 4 years

The question is solved in two parts. First, the value of the $7,000 after 4 years needs to be computed.

Enter the below in a financial calculator to compute the future value:

PV= -7,000

N= 4

I/Y= 8

Press the CPT key and FV to compute the future value.

The value obtained is 9,523.42.

The value of the $7,000 after 4 years is $8,817.98.

Next, the value of the yearly deposit of $4,000 needs to be computed.

Enter the below in a financial calculator to compute the future value of the yearly deposit:

PMT= $4,000

N= 4

I/Y= 8

The value obtained is 18,024.45.

The value of the value of the yearly deposit of $4,000 is $18,024.45.

Therefore, I will have $8,817.98 + $18,024.45= $21,803.58 after 4 years.

B. Information provided:

Yearly payment= $12,000

Time= 10 years

Required return= 15%

The question is solved by calculating the present value.

Enter the below in a financial calculator to compute the present value:

PMT= 12,000

N= 10

I/Y= 15

Press the CPT key and PV to compute the present value.

The value obtained is 60,225.22.

Therefore, I would pay $60,225.22 for the investment.

C. Information provided:

Face value= future value= $100

Coupon rate= 8%/2= 4%

Coupon payment= 0.04*100= $4

Time= 6 years*2= 12 semi-annual periods

Current value= present value= $91.137

The yield to maturity is calculated by entering the below in a financial calculator:

FV= 100

N= 12

PMT= 4

PV= -91.137

Press the CPT key and I/Y to compute the yield to maturity.

The value obtained is 5.

Therefore, the yield to maturity is 5%*2= 10%.

The effective annual yield is calculated using the below formula:

Effective annual yield= (1+r/n)^n-1

Where r is the interest rate and n is the number of compounding periods in one year.

Effective annual yield = (1 + 10/2)^2 – 1

                                          = 1.1025 -1

                                          = 0.1025*100

                                          = 10.25%.

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