Question

You bought an annuity selling at $14,112.74 today that promises to make equal payments at the beginning of each year for the next twelve years (N). If the annuity’s appropriate interest rate (I) remains at 11.00% during this time, then the value of the annual annuity payment (PMT) is__________..

You just won the lottery. Congratulations! The jackpot is $35,000,000, paid in twelve equal annual payments. The first payment on the lottery jackpot will be made today. In present value terms, you really won ____________ —assuming an annual interest rate of 11.00%.

Answer 1

1.Information provided:

Present value= $14,112.74

Time= 12 years

Interest rate= 11%

The question is concerning finding the amount of annuity due. Annuity due refers to annuity that occurs at the beginning of a period.

This can also be 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^ndBGN 2^ndSET on the Texas BA II Plus calculator.

The annual annuity payment is computed by entering the below in a financial calculator in BGN mode:

PV= -14,112.74

N= 12

I/Y= 11

Press the CPT key and PMT to compute the annual annuity payment.

The value obtained is 1,958.33.

Therefore, the annual annuity payment is $1,958.33.

2.Information provided:

Annual payment= $35,000,000 /12 = $2,916,666.67

Time= 12 years

Yield to maturity= 11%

The question is concerning finding the present value of annuity due. Annuity due refers to annuity that occurs at the beginning of a period.

This can also be 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^ndBGN 2^ndSET on the Texas BA II Plus calculator.

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

PMT= 2,916,666.67

N= 12

I/Y= 11

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

The value obtained is 21,019,003.03.

Therefore, the present value is $21,019,003.03.