Actuarial Outpost May 2003 #12
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 Financial Mathematics Old FM Forum

#1
10-28-2007, 09:13 PM
 MrActuary Member Join Date: May 2006 Studying for DMAC... and life Posts: 242
May 2003 #12

I am stumped again. Here is the problem:

Eric deposits X into a savings at time 0, at a nominal rate of interest i, comp. semiannually.

Mike deposits 2X into a different account at time 0, at a simple rate of interest i.

They earn the same interest during last 6 months of 8th year.

Calculate i.

#2
10-28-2007, 09:24 PM
 Gandalf Site Supporter Site Supporter SOA Join Date: Nov 2001 Location: Middle Earth Posts: 31,100

You can do this. For simplicity, let X = 1000 (or keep it as X; if you do it will cancel). How much interest does Eric earn in that 6-month period [in terms of i; or in terms of X and i if you didn't set X =1000].

Hint: calculate Eric's balance at the end of 7.5 years (or at the end of 15 half-years) [again in terms of i, or X and i]. Then the interest he earns in the following 6 months is i/2 times that balance.

Then calculate how much interest Mike earns in 6 months [in terms of i, or of X and i]. Mike gets simple interest, so the interest in every 6 month period is the same. You can use the first 6 months if you like.

Set those two expressions equal. If you kept X until now, the X's will cancel. Solve for i.
#3
10-28-2007, 09:59 PM
 MrActuary Member Join Date: May 2006 Studying for DMAC... and life Posts: 242

Thanks for the prompt reply. I realized that when I was working this I my notation was throwing me off. I was writing "i-upper 2" along with "i" in the same equation, making it looking more difficult than it really was. I finally got my solution to a point where a simple guess and check of the answers could be done very quickly (~8 seconds per answer).
#4
01-20-2011, 04:14 PM
 laraib.usmani Join Date: Jan 2011 College: Undergraduate Posts: 10

i m doing FM paper preparations but have found some difficulties in the following questions.. plz help me regarding these question.. and also explain me the concepts behind them.. Thanks alott

Question 1: Eric deposits X into a savings accounts at time 0, which pays interest at a nominal rate of i, compounded semiannually. Mike deposits 2X into a different saving accounts at time 0, which pays a simple interest at an annual rate of i. Eric and Mike earn the same amount of interest during the last 6 months of the 8th year. Calculate i.

Question 2:Using a method of equated time, a payment of 400 at time t=2 plus a payment of X at t=5 is equivalent to a payment of 400+X at time t=3.3125

At an effective interest rate of 10%, the above two payments are equivalent to a payment of 400+X at time t=k using the exact method. Calculate k.

Question 3: On January 1 1980, Jack deposit 1000 in Bank X to earn interest at the rate of j per annum compounded semi-annually. On January 1 1985, he transferred his account to Bank Y to earn interest at the rate of k per annum compounded quarterly. On January 1 1988, the balance at Bank Y in 1990.76

If Jack could have earned interest at the rate of k per annum compounded quarterly from January 1 1980 through Jan 1 1988, his balance would have been 2203.76

Calculate the ration k/j.

These r the three questions which im trying to understand but im not getting them.. Please help me regarding these questions

Regards,
#5
02-28-2012, 04:45 PM
 zzzsilver Member Join Date: Aug 2011 College: MIT Posts: 151
stumped

Hi, I still don't understand why you owuld multiply the (i/2) by the amount that is in the account after 7 1/2 years to find the interest earned in the last 6 months of the 8th year. Can someone explain how that works out? Thanks!

Z
__________________
P FM
Lookin at the world through rose colored glasses .
#6
02-28-2012, 04:53 PM
 Gandalf Site Supporter Site Supporter SOA Join Date: Nov 2001 Location: Middle Earth Posts: 31,100

That's just the definition of nominal interest, compounded semiannually. If my rate is 8% nominal, compounded semi-annually, then in 6 months I earn 4% on the balance at the start of the 6 month period.

(That assumes that the starting date is right after an interest-compounding period, which in this problem it is.)
#7
02-28-2012, 04:59 PM
 zzzsilver Member Join Date: Aug 2011 College: MIT Posts: 151
oh

Oh ok it makes sense now that you put numbers to it. the (i/2) was throwin me off but I get it now, thanks.

Z
__________________
P FM
Lookin at the world through rose colored glasses .
#8
05-25-2018, 01:03 PM
 actsci123451 SOA Join Date: Feb 2018 Posts: 11

if the account pays simple interest at an "annual rate of i," I know that the interest is constant every year, but is it constant every half year as well?