# CF Sum Problem

Q: A saver deposits the following amounts in an account paying a stated annual rate of 4%, compounded semiannually:

Year** End of Year Deposits (\$)**

1 4,000

2 8,000

3 7,000

4 10,000

Q. At the end of Year 4, the value of the account is closest to:

1. \$30,432
2. \$30,447
3. \$31,677

I enter CFo = 0 , C01 = 4,000 F01 = 1 …… C04 = 10,000 F04 = 1 I = 4/2 = 2 I am getting 27,445.63

Looks like you calculated the present value, not the future value. What’s 27445.63 * 1.02^8?

You were right, I calculated the NPV, but even after computing NFV in BA II Plus Prof., my answer was 29708.03200

And I tried solving it the other way around, by multiplying 27445.63 * 1.02^8, but still the answer is not correct.

To use 2%, you have to insert 0 cashflows between times 1,2 3, and 4

CF0=0, C01=0 F01=1 C02=4000 F02=1, C03=0 F03=1, C04= 7000 F04=1, etc.

Alternatively, you could use I=4.04 = 1.02^2-1 in your first post.

Answer is B using either method.

I just showed a mate today this problem lol

I would first convert the i using EAR formula:

in HP12C: 0,04 enter 2 / 1 + 2 yx 1 - 100x

You would get i = 4,04

now

0g CFO

4000 CHS g CFj

8000 CHS g CFj

7000 CHS g CFj

10000 CHS g CFj

4,04 i

f NPV = 25.986,14192

now:

PV = 25.986,14192 CHS

i = 4,04

N = 4

PMT = 0

FV = 30.446,90696

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The EAR is not 4.04%; it’s 2.0184% (= [1 + (2% / 12)]12 − 1).

Edit: wrong TVM question. Sorry.

Can you explain why?

Because as we are compounding semianually I think the number of compounding periods its divided and elevated by 2 and not 12…

If the EAR is 2,0184% how would you solve the rest of the question?

You must be thinking of another TVM question: lotsa them flying around these here parts today!!!

Because:

Oops!

^ We should go for margaritas!!!

Thank you so much!!

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