Accounting Question - Discounting an Annuity. (1 Viewer)

[SoCal]

Can someone please help me out with this question? How much was borrowed if payments are $200 every quarter over 5 years and interest is 8%p.a. for the first 3 years and 12%p.a. for the last 2 years? I know you use this equation:

P = C/i [1-(1/{1+i}^n)]

Now, I know that the first line is this:

P = 200/0.02 [1-(1/{1.02^12})] + [200/0.03 [1-(1/{1.03^8})]] / 1.02^12

I understand everything except for why the second half of the equation (i.e. [200/0.03 [1-(1/{1.03^8})]]) is divided by 1.02^12. So can someone help me out and explain to me why this is the case? Thanks.

 

[SoCal]

If you can get that one, I would appreciate it if you could explain these two to me as well:

Deferred Annuity

What sum of money must be set aside at child's birth to provide for 6 half-yearly payments of $1,500 to help with the cost of tertiary education.
Assume the first payment is made on the child's 19th birthday and interest is 8%p.a. compounded semi-annually.

You use the same equation as above and the first line is:

P = [1,500/0.04 [1-(1/{1.04^6})]] / 1.04^37

Now, again I understand everything except for why the second whole equation is divided by 1.04^37.


Perpetuity

How much money is needed to establish a scholarship fund paying $2,000 half-yearly forever if interest rate is 6%p.a. compounded half-yearly and the first payment is at the end of year 2?

The final answer is $61,009.75 but I have no idea how to get that answer.

Once again any help would be appreciated.

 

[jlh]

for your first question, i got 3156.05
i didn't use your working out cuz i don't udnerstand it...

heres what i did:
first i had to convert the interest rates. they were given as yearly interest rates but payments were every quarter, so you'd have to convert them to quarterly interest rates. 8% is equal to 0.019426456 and 12% is 0.028737344.
then i put it into the formula as follows:
200((1-1.017426546^-12)/(0.019426546)) + 200((1-1.028737344^-8)/(0.02737344))*(1.017423546)^-11

 

[SoCal]

for your first question, i got 3156.05
i didn't use your working out cuz i don't udnerstand it...

heres what i did:
first i had to convert the interest rates. they were given as yearly interest rates but payments were every quarter, so you'd have to convert them to quarterly interest rates. 8% is equal to 0.019426456 and 12% is 0.028737344.
then i put it into the formula as follows:
200((1-1.017426546^-12)/(0.019426546)) + 200((1-1.028737344^-8)/(0.02737344))*(1.017423546)^-11

The answer is actually $3,222.27. What equation are you using there? I don't follow it. I think where you went wrong is that the 8%p.a. converts to 2%p.q. and 12%p.a. converts to 3% p.q. I think you were maybe converting it to its effective interest rate, which you aren't supposed to do.

 

[Halo]

These are finance questions (not accounting).

For the first question, the second half of the equation is divided by 1.02^12 because you need to discount that part of the annuity to the beginning of the first year. If you do not, you are only working out its present value to the beginning of the fourth year (which is not what the question wants).

For the second question, you must remember that the formula only discounts to the half-year of the child's 18th birthday (i.e. one period, which is semi-annual in this case, before the first payment). To discount this annuity back to the birth of the child (i.e. to bring the present value to the beginning of the first period), you need to discount all that by (18*2)+1 = 37 periods.

If you still do not get it, I can work out the numbers for you later...

For the third question, use the perpetuity formula which will work out the present value to one period before the first payment (i.e. the mid-year of year 2). This gives you 2000/(0.06/2) = 66666.67. You now need to discount this value to the date of the establishment of the fund (i.e. beginning of the first period), which is 66666.67/((1+(0.06/2))^3) = 61009.44.

 

[SoCal]

These are finance questions (not accounting).

Really? Well I said it was an Accounting question because we are learning it in Accounting.

For the first question, the second half of the equation is divided by 1.02^12 because you need to discount that part of the annuity to the beginning of the first year. If you do not, you are only working out its present value to the beginning of the fourth year (which is not what the question wants).

I see. Thanks.

For the second question, you must remember that the formula only discounts to the half-year of the child's 18th birthday (i.e. one period, which is semi-annual in this case, before the first payment). To discount this annuity back to the birth of the child (i.e. to bring the present value to the beginning of the first period), you need to discount all that by (18*2)+1 = 37 periods.

If you still do not get it, I can work out the numbers for you later...

I see, so it is similar to the first question. Is the reason why you don't originally discount it back 37 periods because you only pay the $1,500 for six periods?

For the third question, use the perpetuity formula which will work out the present value to one period before the first payment (i.e. the mid-year of year 2). This gives you 2000/(0.06/2) = 66666.67. You now need to discount this value to the date of the establishment of the fund (i.e. beginning of the first period), which is 66666.67/((1+(0.06/2))^3) = 61009.44.

OK, I can see that now. Thank you so much for all your help.