QMA tute question 5 (week 3) (1 Viewer)

[miffytoki]

ARGH!! i'm really frusterated!

anyone done this question and got the answer in the textbook?

the question is

HP 5.2, problem 15, p226)

A debt of $600 due in 3 yrs and $800 due in 4 years is to be repaid by a single payment 2 yrs from now. if the interest rate is 8% compounded semi-annually, how much is the payment?

answer: $1238.58

i don't get how the amount u're repaying all up can be less than the total debt put together (600 +800) ...

Help please!

 

[t-i-m-m-y]

Okay.. I'll try and help

First of all, lets find the effective annual rate of interest.. this is given by i=(1+0.08/2)^2 - 1, which according to my trusty windows calculator is 0.0816 or 8.16% pa.

Now for the debt.. it is paid in 2 year times

First of all, lets look at the 600 debt. This is due in 3 years, so the 600 is paid in 3 years.. but that means at t=0 (now) it is not worth 600 dollars yet, we need to discount it.. If we discount it to t=2(which is when we repay it), we discount by 1/1.0816 giving, a present value at t=2 of the debt as 600/1.0816=554.73

Similarly, we discount the 800 debt by 2 time periods, ie 800/1.0816^2 = 683.84

Add the two together, and you get 1238.57(which is close enought to your answer)

The theory behind this is that 1 dollar now can earn interest of say i%, giving you 1+i at the end of one year.. therefore the debts are not worth 600 or 800 dollars now, that is what they are worth at the end of 2,4 years respectively... and they would actually be worth less at t=0 etc...

Hope that helps..

 

[miffytoki]

thank u heaps!

 

[nufc-26]

First of all, lets look at the 600 debt. This is due in 3 years, so the 600 is paid in 3 years.. but that means at t=0 (now) it is not worth 600 dollars yet, we need to discount it.. If we discount it to t=2(which is when we repay it), we discount by 1/1.0816 giving, a present value at t=2 of the debt as 600/1.0816=554.73

sorry, i dont understand this part.....
how come its not 600/(1.0816)^2 ??????
the solutions are different to how u did it timmy,can someone pls explain?

thanks

also... what was the answer for q7???

 

[Grizzly]

hope this helps....

Notice time periods are represent in "HALF YEARS"

i.e, debt due at end of year 3 - is shown as "TIME = 6" .. ( 3 years x 2 )

Set focal date at TIME = 4 (End of 2 years)

i.e, Bring this payment (as well as the debt due at TIME 8) BACKWARDS.

i.e, USE PRESENT VALUE formula.
[Refer to image]

Why is the value LESS than 600+800 ?

Imagine you invested a sum of money that will accumulate to repay the debt of 1400 at time 8.
Obviously, this investment will grow due to compound interest etc.
i.e, you would require a PRESENT VALUE smaller than 1400 to grow to a figure around this amount.

 

[Grizzly]

also... what was the answer for q7???

a. 1411.02

 

[nufc-26]

thanks for the explanation Grizzly,
i managed to get the answer before reading the post though...

 

[t-i-m-m-y]

Grizzly: yeah u can use half-years, i just converted to an annual effective rate..gives same answer

And no I didn't do QMA, so i'm not sure how u guys do it

 

[Grizzly]

Grizzly: yeah u can use half-years, i just converted to an annual effective rate..gives same answer

Yup. The only reason why i converted to half years because it is compunded semi-annually.