Reading 6 Practice Problem Q 15

CFA Level I Quant
#1

Question 15:
For a lump sum investment of ￥250,000 invested at a stated annual rate of 3% compounded daily, the number of months needed to grow the sum to $1,000,000 is closest to ：

The correct answer is A. 555

However, the numbers don’t add up if I use the following formula:

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In this N is “how many years required”. The textbook states the answer is 46.21 years (equivalent to 555 months). But if we replace 46.21 with N in the above formula, the equation is incorrect.

This is killing me… anyone can help please?

For a lump sum investment of ¥250,000 invested at a stated annual rate of 3% compounded daily
#2

I got 46.2116.

250,000\times\left(1 + \frac{3\%}{365}\right)^{365\times46.21} = 250,000\times\left(1 + \frac{3\%}{365}\right)^{16,866.65}
= 250,000\times\left(3.9998\right) = 999,952.37

Close enough.

#3

Thank you so much for your reply!! I did the calculation again and arrived at the same result as you. I don’t know why I kept getting the wrong result before…

Do you mind me asking you, if you know how to use the financial calculator to get N in this equation:

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I had to try the 3 choices individually to see which one adds up, as I don’t know how to get N directly… Thank you in advance for your kind help!

#4

Actually, you need to check only one: the middle one.

Suppose that your choices were, say:

A. 555 months
B. 575 months
C. 605 months

You check the middle number (always choice B). If the formula works out to 1,000,000 (or really close), then B is correct. If it’s too big, then 575 is too big; the answer is A. If it’s too small, then 575 is too small; the answer is C.

Here, if you try 575, you get 1,052,477. That’s too big, so 575 is too big: the answer is 555 months.

If you really want to solve for n:

250,000\times\left(1 + \frac{3\%}{365}\right)^{365n} = 1,000,000
\left(1 + \frac{3\%}{365}\right)^{365n} = \frac{1,000,000 }{250,000} = 4
ln\left[\left(1 + \frac{3\%}{365}\right)^{365n}\right] = ln\left(4\right)
\left(365n\right)ln\left(1 + \frac{3\%}{365}\right) = ln\left(4\right)
n = \frac{ln\left(4\right)}{365ln\left(1 + \frac{3\%}{365}\right)}
#5

Thank you so much! That’s very smart!

Now I can sleep well today:p Have a great weekend!

#6

On the BAII

P/Y=1. C/Y= 365
I 3 PMT 0 PV 250000 FV -1000000 CPT N 46.21171104

#7

Cool!