In: Finance

1. Bankers trust has bonds maturing in 27 yrs. the total principal that must be repaid by the bank at that time is $950 million. The relevant discount rate is 7.5% per yr. what is the present value of this liability assuming quarterly compounding?

2. Comparing two annuities which offer monthly payments of $1,750 for 10 yrs and pay interest at an annual rate of 4.5%. Annuity A will pay you on the 1st day of each month while B will pay on the last day of each month. Which one of the following statements is correct?

A. Annuity b is an annuity due

b. Annuity b has smaller future value than A

c. Both have different present values as of today and equal future values at the end of year 10.

D. Both have equal present values but unequal futures values at the end of yr 10

1.Information provided:

Future value= $950 million

Time= 27 years*4= 108 quarters

Discount rate= 7.50%/4= 1.8750%

Present value is calculated by entering the below in a financial calculator:

FV= 950

N= 108

I/Y= 1.8750

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

The value obtained is 127.7675.

Therefore, the present value of the liability is **$127.77
million.**

2. Monthly payment= $1,750

Interest rate= 4.50%/12= 0.3750% per month

Time= 10 years*12= 120 months

Annuity A is an annuity due since it is paid out in the beginning of the month.

The future value of annuity due is solved using a financial calculator by inputting the below into the calculator:

The financial calculator is set in the end mode. Annuity due is
calculated by setting the calculator to the beginning mode (BGN).
To do this, press 2^{nd} BGN 2^{nd} SET on the
Texas BA II Plus calculator.

The below has to be entered in a financial calculator:

PMT= 1,750

N= 120

I/Y= 0.3750

Press CPT and FV to calculate the future value of ordinary annuity.

The value obtained is $265,588.8663

The future value of annuity due is $265,588.87.

Annuity B is an ordinary annuity since the payment is made at the end of

The future value of ordinary annuity is calculated with the help of a financial calculator.

The below has to be entered in a financial calculator:

PMT= 1,750

N= 120

I/Y= 0.3750

Press CPT and FV to calculate the future value of ordinary annuity.

The value obtained is $264,596.6289.

The future value of ordinary annuity is $264,596.63.

Therefore, **statement b** is correct.

In case of any query, kindly comment on the solution

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