Actuarial Outpost FM2 Problem
 User Name Remember Me? Password
 Register Blogs Wiki FAQ Calendar Search Today's Posts Mark Forums Read
 FlashChat Actuarial Discussion Preliminary Exams CAS/SOA Exams Cyberchat Around the World Suggestions

 Enter your email to subscribe to DW Simpson weekly actuarial job updates. li.signup { display: block; text-align: center; text-size: .8; padding: 0px; margin: 8px; float: left; } Entry Level Casualty Health Life Pension All Jobs

 Financial Mathematics Old FM Forum

 Thread Tools Search this Thread Display Modes
#1
05-11-2019, 04:35 PM
 jubair07 Member SOA Join Date: Jan 2016 Studying for Exam IFM College: BEng Aerospace Engineering Posts: 158
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?
__________________
Exam P Exam FM IFM
#2
05-11-2019, 04:47 PM
 career changer 2 Member Join Date: Mar 2011 Posts: 318

10 * (1-3x) + 5 * (1-6x) = 12

Discount, not interest rate. It's been forever since I've done these. Hope that's right.
#3
05-11-2019, 04:53 PM
 jubair07 Member SOA Join Date: Jan 2016 Studying for Exam IFM College: BEng Aerospace Engineering Posts: 158

Quote:
 Originally Posted by career changer 2 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!
__________________
Exam P Exam FM IFM
#4
05-12-2019, 05:01 PM
 jubair07 Member SOA Join Date: Jan 2016 Studying for Exam IFM College: BEng Aerospace Engineering Posts: 158

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!
__________________
Exam P Exam FM IFM
#5
05-12-2019, 05:05 PM
 Academic Actuary Member Join Date: Sep 2009 Posts: 8,925

6% is the nominal, not the effective rate. You are working in quarters so the effective rate per quarter is 1.5%.
#6
05-12-2019, 05:13 PM
 jubair07 Member SOA Join Date: Jan 2016 Studying for Exam IFM College: BEng Aerospace Engineering Posts: 158

Quote:
 Originally Posted by Academic Actuary 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"
__________________
Exam P Exam FM IFM
#7
05-14-2019, 03:55 PM
 jubair07 Member SOA Join Date: Jan 2016 Studying for Exam IFM College: BEng Aerospace Engineering Posts: 158

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?
__________________
Exam P Exam FM IFM
#8
05-14-2019, 04:42 PM
 Gandalf Site Supporter Site Supporter SOA Join Date: Nov 2001 Location: Middle Earth Posts: 31,286

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.
#9
05-14-2019, 05:00 PM
 jubair07 Member SOA Join Date: Jan 2016 Studying for Exam IFM College: BEng Aerospace Engineering Posts: 158

Quote:
 Originally Posted by Gandalf 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)?
__________________
Exam P Exam FM IFM
#10
05-14-2019, 05:22 PM
 Gandalf Site Supporter Site Supporter SOA Join Date: Nov 2001 Location: Middle Earth Posts: 31,286

Yes

 Thread Tools Search this Thread Search this Thread: Advanced Search Display Modes Linear Mode

 Posting Rules You may not post new threads You may not post replies You may not post attachments You may not edit your posts BB code is On Smilies are On [IMG] code is On HTML code is Off

All times are GMT -4. The time now is 10:55 AM.

 -- Default Style - Fluid Width ---- Default Style - Fixed Width ---- Old Default Style ---- Easy on the eyes ---- Smooth Darkness ---- Chestnut ---- Apple-ish Style ---- If Apples were blue ---- If Apples were green ---- If Apples were purple ---- Halloween 2007 ---- B&W ---- Halloween ---- AO Christmas Theme ---- Turkey Day Theme ---- AO 2007 beta ---- 4th Of July Contact Us - Actuarial Outpost - Archive - Privacy Statement - Top