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

For an annuity due, change BA II Plus settings and put it to BGN mode by using following keystrokes:

2nd - PMT - 2nd - ENTER - 2nd - CPT

Now, to calculate the future value of annuities:

For July 1: PV = 0, N = 10, PMT = -1000, I/Y = 5,

Compute FV = 13,206.79

After 10 years, this will be equal to : 13,206.79 * (1.05) ^ 10 = 21512.47

For January 1:

PV = 0, N = 10, PMT = -2000, I/Y = 5

Compute FV = 26413.57

Since the first annuity is received 6 months from now, this amount will be compounded for 9.5 years and not 10.

FV = 26413.57 * (1.05) ^ 9.5 = 41988

Sum of annuities: 21512.47 + 41988 = 63,500