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Old 05-11-2019, 04:35 PM
jubair07 jubair07 is offline
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Default FM2 Problem

A loan of 12 is to be repaid with payments of 10 at the end of 3 years and 5 at
the end of 6 years. Calculate the simple discount rate that is being charged
on the loan.

I did: 10/(1+3x) + 5/(1+6x) = 12

i = 6.405%. Should be pretty straightforward. But Finan's book says 5%. Where did I go wrong?
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Old 05-11-2019, 04:47 PM
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10 * (1-3x) + 5 * (1-6x) = 12

Discount, not interest rate. It's been forever since I've done these. Hope that's right.
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Old 05-11-2019, 04:53 PM
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Quote:
Originally Posted by career changer 2 View Post
10 * (1-3x) + 5 * (1-6x) = 12

Discount, not interest rate. It's been forever since I've done these. Hope that's right.
Thanks. How silly of me!
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Old 05-12-2019, 05:01 PM
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Q. Find the present value of an annuity which pays $200 at the end of each
quarter−year for 12 years if the rate of interest is 6% convertible quarterly.

My answer: 200 x An
An= 1-1/(1.015)^48 / 0.0146738 (which is nominal i4).

The answer on the book is based on effective rate/4 = i/4 = 0.015

Can anyone please explain why it is using nominal 1.015^4 = 1.0614 instead of 1.06 on top but effective rate of i/4 at the bottom?

Thanks!
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Old 05-12-2019, 05:05 PM
Academic Actuary Academic Actuary is online now
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6% is the nominal, not the effective rate. You are working in quarters so the effective rate per quarter is 1.5%.
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Old 05-12-2019, 05:13 PM
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Quote:
Originally Posted by Academic Actuary View Post
6% is the nominal, not the effective rate. You are working in quarters so the effective rate per quarter is 1.5%.
Thanks. Didn't realise the "6% convertible quarterly"
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Old 05-14-2019, 03:55 PM
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Q: Smith borrows $5,000 on January 1, 2007. He repays the loan with 20 annual payments, starting January 1, 2008. The payments in even-number year are 2X each; the payments in odd-number years are X each. If d = 0:08; find the total amount of all 20 payments? I have seen some problems but

I did it by considering two separate payment streams.

One of X for each year at i= 1/(1-0.08) - 1 = 0.086956
Another one every two years of X at j = (1+i)^2-1 = 0.18147

X a(20|i) + X a(10|j) = 5000

a(20|i) =9.330
a(10|j) = 4.47064
Solving, X = 362.301

Total = 362.301 x 30 = 10869.03

Answer on the book = 10571.40

I looked up similar problems online, but can't seem to figure out. Where did I go wrong?
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Old 05-14-2019, 04:42 PM
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Odd numbered years are like 2009, 2011, etc. So the first double payment is one year fom the loan date. Your method has it two years from then. You need to multiply your 4.46064 by 1.086956.
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Old 05-14-2019, 05:00 PM
jubair07 jubair07 is offline
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Quote:
Originally Posted by Gandalf View Post
Odd numbered years are like 2009, 2011, etc. So the first double payment is one year fom the loan date. Your method has it two years from then. You need to multiply your 4.46064 by 1.086956.
Thanks. Just to ask if you can clarify how multiplying with (1+i) helps. Is it to do with moving the first payment date from 2008 to 2007 by 1 year so payment of a(10|j) starts 1 year earlier?

So, if I want to move it by 2 years, then it will be multiplying by (1+j)?
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Old 05-14-2019, 05:22 PM
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Yes
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