Future value of a delayed annuity

3)Two years from now, a client will receive the first of three annual payments of $20,000 from a small business project. If she can earn 9 percent annually on her investments and plans to retire in six years, how much will the three business project payments be worth at the time of her retirement?

year 2 - $20.000 year 3 - $20.000 year 4 - $20.000 year 6 - retirement i = 9

y2f = $28.231,63 y3f = $25.900,58 y4f = $23.762,00 sum = $77.894,21

Basicly I solved this problem with my HP12c, but I had to do one by one cash flow, means that I did:

20000 CHS PV

9 i

4 N

0 PMT

FV = $28.231,63,

But if the problem asked too many cash flows it would take so much time to do them, does anyone know another method with the HP12c?

Calculate the NPV, then the future value of that NPV.

Easy peasy.

Can you show me step by step how?

I tried

0 g CF0

0g CFj

20000 CHS g CFj

3 g NJ

0 g CFj

0g CFj

9i

f NPV,

I got 46.445,77, I should have got 65.562,00…

Wait It`s actually right, the book does it a different way that IDK how is the method that was the done in the book…

If they want the accumulated value of the payments at time 6, I would treat the 3 payments as an annuity due and calculate the FV at time 5. Bump that up with another year’s interest to get the value at time 6:

Use BGN mode

N 3 I 9 PMT 20000 CPT FV 71,462.85

Multiply 71462.85 by 1.09 = 77,894.21

46,445.77 is the present value at time 0 of the payments at times 2,3, and 4.

46,446 is correct for the NVP.

Now, put that in as the PV, i = 9%, n = 6, PMT = 0, and solve for FV.

There are many ways you can approach this. The best way to start any of them is to draw a time line.

Yes Im seeing, Im solving the end chapter questions from reading 6 from quant. methods, and Im getting so confused with some questions :frowning_face: