TVM Problem!

CFA Level I
#1

You want to have $1,000,000 in 10 years to fund your retirement. You plan to make annual contributions at the end of each year into an investment account that earns an annual interest rate of 8%. The first contribution will be made at the end of the current year. How much should each annual contribution be to achieve your goal?

#2

How do you think you should solve this?

#3

FV = 1,000,000
I = 8%
N = 10
Pmt = 69K???

1 Like
#4

PV = ?

Do you think that that’s wrong?

Is it reasonable?

#5

I’m stumped as to why I need to calculate the present value (PV) when making annual contributions. Since each annuity would earn an 8% interest and compound, isn’t that sufficient?

#6

You don’t need to calculate the PV; you need to input the PV into your calculator to calculate the payment. (You didn’t specify any input for PV.) You’ll need a smaller payment if you start with $500,000 than if you start with $0.

Back to the questions:

  • Do you think that an annual payment of $69,000 is incorrect? Why or why not?

  • Do you think that it’s reasonable? Why or why not

#7

Since there is no mention of a starting account value, I would treat PV as 0.

#8

Only because, on this occasion at least, you’re rational.

#9

When I read the question, I did not assume a PV was necessary.

Back to the questions:

Do you think that an annual payment of $69,000 is incorrect? Why or why not?

  • I thought it was a rough estimate: 70k10 =7001.08^10. $1.5M

    Do you think that it’s reasonable? Why or why not

  • As breadmaker said. I thought pv was 0.

#10

Only in the sense that your calculator might already have some other value for PV, which will scupper your calculation.

Putting in all four inputs – even those that are zeroes – is a good habit to cultivate.

#11

I still get $69,029.49.

I saw an answer where they PV the million. What am I missing?

#12

You’re not missing anything; $69,029.49 is the correct answer.

All I’m saying is that when you do problems such as this, always put four inputs into your calculator, whether they’re zero or not. If you’re solving for:

  • FV, put in values for PV, PMT, i and n
  • PV, put in values for FV, PMT, i and n
  • PMT, put in values for PV, FV, i and n
  • i, put in values for PV, FV, PMT, and n
  • n, put in values for PV, FV, PMT, and i
#13

If you have a non-zero starting amount, then you would enter that value in PV. To borrow from Magic Man’s example, if you had $500,000, you would enter -500,000 as PV, 1,000,000 FV 10 N I 8.

ETA: It’s odd that there was a PV mentioned in a solution you saw. The PV of the annual deposits is 463193.50, which compounded at 8% annually for 10 years will also get you to $1,000,000 at time 10. Maybe the author was trying to demonstrate that equivalence. :man_shrugging:

#14

I put the answer in ChatGPT, and it gave me $46k with a brilliant explanation. I tried it a couple of times, and it consistently provided the same answer. It caught me off guard. Had me second guessing myself.

Thank you for your help!