Question

Dino wins a lottery on July 1. His prize is an annuity due with 10 payments of $1,000 each July 1(starting with the day he wins) and 10 payments of $2,000 each January 1. If this annuity is valued at an effective annual interest rate of 5% what is the accumulated value of this prize (the combined value of the two annuities) exactly twenty years after he wins it? Please use the BA II Plus calculator to show your work.

Answer 1

On BA II PLUS CALCULATOR

Insert,

PMT= 1000

N=10

I/Y= 5%

then CPT, PV

The answer will be for Ordinary Annuity, PV= 7721.73

For calculating Annuity Due, multiply with r=5%, PV= 7721.73 (1+R)

PV= 7721.73 (1+ 0.05)

PV= 7721.73 (1.05)

PV= 8107.82

Then again placing the values in BA II PLUS Calculator,

PV= -8107.82

N=20

I/Y= 5

PMT= 0

CPT FV

FV= 21512.46 (This value will be at the end of 20 years for Annuity Due payment of $1000)

Again for $2000, on BA II PLUS CALCULATOR, as the payment for $2000 will start at the end of 10 years.

PMT= 2000

I/Y= 5%

PV=0

N=10

CPT FV

FV= 25155.78 (THIS VALUE WILL BE AT THE END OF 20 YEARS FOR $2000)

for annuity due multiply the above FV with (1+r) i.e. (1+0.05)

FV= 25155.78 * (1.05)

FV = 26413.57

Now adding both the future values

FV = 21512.46

FV= 26413.57

ANSWER OF FV at the end of 20 years = 47926.03