A client invests €20,000 in a four- year certificate of deposit (CD) that annually pays interest of 3.5%

CFA Level I Quant
#1

A client invests €20,000 in a four- year certificate of deposit (CD) that annually pays interest of 3.5%. The annual CD interest payments are automatically reinvested in a separate savings account at a stated annual interest rate of 2% compounded monthly. At maturity, the value of the combined asset is closest to:

PV = $20.000 CHS i = 3,5 N = 1 PMT = 0 FV = $20.700

so at end of each year you will get $700 dollars from this CD

year 1

PV = 700 CHS n = 3*12 = 36 i = 2/12 = 0,166666667 PMT = 0 (ask)FV = $743,25

year 2

PV = 700 CHS n= 2*12 = 24 i = 2/12 = 0,166666667 PMT = 0 FV = $728,54

year 3

PV = 700 CHS n = 12 i = 2/12 = 0,166666667 PMT = 0 FV = $714,13

year 4

$700

sum = 20.000 + 743,25 + 728,54 + 714,13 + 700 = $22.885,92

My question is, is there any way to do a question like this faster?

because to do the 4 years take all these calculations above and this took so much time…

Anyone else knows a faster way?

#2

The coupon payments are an annuity.

Use the TVM buttons to determine the future value of that annuity, then add that to the par value of the CD.

#3

Could you show me how would you do it on HP12c?

#4

No.

But you can show me.

What are the annual payments?

How many payments are there?

What is the interest rate that those payments will earn?

What’s the PV? (Be careful on this one; remember, we’re dealing only with the interest payments here.)

Calculate FV (i.e., let the calculator do it for you).

Add the face value of the CD.

That’s the total future value.

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#5

Not sure about HP Buttons but think of this way:

you have 4 payments of 700 earning 2% per annum, with payments being made at the end of the period, being deposited into an account that starts off at 0.

PV = 0 , N = 4 , PMT = 700, I/Y = 2% - CPT FV.

FV + 20,000 = value of combined asset.

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#6

Since the second account is compounded monthly, it does not earn 2% between payments. If actually earns 2.0184% (i.e. the effective annual rate).

One of the key concepts is that you must always match the interest rate to the period. If you have an annuity with ANNUAL payments, you must use the interest earned IN A YEAR’S TIME. So, while the solution by Paul is otherwise correct, I/Y should be 2.0184%

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#7

Thanks.

That’s what I was hoping he would do.

(While getting the interest rate correct, of course; see busprof’s post, above.)

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#8

The thing is that is compounded month, doing this way you would assume it would pay in the end of the year which wouldn`t match exactly…

#9

You can use the EAR formula:

(1 + Periodic Rate)12 - 1

(1 + 0,02/12)12 - 1

(1 + 0,00167)12 - 1

1,0016712 - 1

1,02018436-1

EAR = 0,02018436

With this way it would work, through I wanted to do a way that didnt require this conversion formula, thats why I made this topic…

#10

PV = 0 , N = 4 , PMT = 700, I/Y = 2% - CPT FV.

as Paul said, the thing is I can`t use 2 as i, you would need to convert it to EAR. I wanted to know a method without having to convert it…

like using 36 N something like that…(as its montly wining from the $700, it wouldnt made any win on the first year cuz the first payment wouldnt exist first year (thats why im thinking of 36 N not 48…)

#11

There is a way to keep the 2% monthly rate, but it’s not on the CFA syllabus. Trust me on this one: the EAR approach is much simpler to deal with. :+1:

To use 2% monthly, you need to use an annuity formula where the compounding frequency is greater than the payment frequency:

Step 1 N 48 I 2/12 PMT 1 CPT FV -49.92896

Step 2 N 12 I 2/1/2 PMT 1 CPT FV -12.11061

FV using 2% monthly = 700 * 49.92896 / 12.11061 = 2,885.92079

#12

Damn, yeah this looks way harder :confused:

Guess I will have to remember the EAR formula :+1:

Like now I`m fresh with this formula cuz I just finished the reading but will not be that easy to remember after times pass by…

I think It`s a really important formula to know in the exam through :bulb:

Thanks.

#13

Go make us proud!!! :+1: :kiss:

#14

hey
That really simplifies it but I wanted to understand how do you take N=4, since the 700 will be paid at year 1 end which leaves only 3 years until year 4 end.

#15

On further reflection, it can be done on the BAII:

P/Y=1 C/Y=12
END
2nd CLR TVM
4 N 2 I -700 PMT CPT FV 2,885.92

I have no idea why I didn’t just go straight to this.

#16

Why would we use TMV method, but not CFs in the calculator. When I tried to get the NPV of the 700 payments with CFs I get the wrong answers. Can someone explain me why, please?

#17

The payment is level, evenly spaced, and the interest rate is the same across all years. The TVM worksheet was made precisely for this kind of problem!!!

Are you referring to the CF worksheet? It would be a royal pain to set up not just for CFs (monthly vs annual), but for the interest rate to use as well (2%/12 for monthly or 2.0184% effective annual); older versions of the BAII don’t have the ability to calculate FV of the CF values. You should get the exact same answer as with TVM, but you would burn up valuable time in an exam!!!