Help!!! Qma Past Paper Question!!! (1 Viewer)

[studymon]

Could someone please show me a working to this question??

An amount of 20,000 was invested at 5.8% p.a. compounded daily for one year then at 6.6% p.a. compounded continuously for two years. What was the annual effective rate earned for the three years?

the answer is: 6.538%

thanks,,
studymon

 

[studymon]

oh and how about this question??

Sonia bought a 320,000 apartment and financed it with a mortgage over 20 years. She made payments at the end of each month and the interest rate was 7.5% p.a. compounded monthly. After 3 years she needs to sell the apartment because the interst rate is about to rise to 8.5% p.a. (still compounded monthly.) how much does she now owe??

ans. $296,750.36


it'd be greatly appreciated even if you only told me what steps i should take to solve this problem =]!!

thanks,,
studymon

 

[dm4n]

first q : (1+re)3 = (1.0001589)365 * (1.0682267)2 u get 1.0682267 from e0.066
(1+re) = 1.06538

second q: R=320000* 0.00625/1-(1.00625)-240
= 2577.90
then 2577.90* 1-(1.00625)-204 / 0.00625 to get the principal outstanding

i need help with this question:
A businessman leases a car for 3 years. He makes 36 monthly payments of $850, beginning on the day the lease is signed, plus a final payment of $12200 on the day the lease is terminated to take ownership of the car. If interest is charged at 10.2% p.a. compounded monthly, what is the original cost of the car?

answer: $35,484.85

 

[3unitz]

i need help with this question:
A businessman leases a car for 3 years. He makes 36 monthly payments of $850, beginning on the day the lease is signed, plus a final payment of $12200 on the day the lease is terminated to take ownership of the car. If interest is charged at 10.2% p.a. compounded monthly, what is the original cost of the car?

answer: $35,484.85

you need to take into consideration the payment each month along with the interest.

let,
A = amount owing
C = original cost of car

on the day: A = C - 850
in 1 month: A = (C - 850)1.0085 - 850
in 2 months: A = [(C - 850)1.0085 - 850]1.0085 - 850
...
in 36 months: A = C(1.0085)^36 - 850(1.0085)^36 - 850(1.0085)^35 - ... - 850(1.0085) - 12200
also, since this is the final payment we know A must equal 0.

0 = C(1.0085)^36 - 850[(1.0085) + (1.0085)^2 + ... + (1.0085)^36] - 12200
0 = C(1.0085)^36 - 850[1.0085 - (1.0085)^37] / (1 - 1.0085) - 12200

solve for C,

C = $35,484.85

 

[dm4n]

^ thanks champ

 

[studymon]

ahh thanks heaps dm4n!!!

 

[studymon]

one question, ...for this:

Sonia bought a 320,000 apartment and financed it with a mortgage over 20 years. She made payments at the end of each month and the interest rate was 7.5% p.a. compounded monthly. After 3 years she needs to sell the apartment because the interst rate is about to rise to 8.5% p.a. (still compounded monthly.) how much does she now owe??

ans. $296,750.36




why dont you get the same answer if you first find the R when A = 320000 and r = 0.075/12 then find the S for the 3 year payment then minus that amount from 320,000??

dm4n used principal outstanding....what is the difference??

 

[studymon]

and another thing, ..why isnt the 8.5% used in the question?? ...in reference to dm4n's worked solution

 

[studymon]

you need to take into consideration the payment each month along with the interest.

let,
A = amount owing
C = original cost of car

on the day: A = C - 850
in 1 month: A = (C - 850)1.0085 - 850
in 2 months: A = [(C - 850)1.0085 - 850]1.0085 - 850
...
in 36 months: A = C(1.0085)^36 - 850(1.0085)^36 - 850(1.0085)^35 - ... - 850(1.0085) - 12200
also, since this is the final payment we know A must equal 0.

0 = C(1.0085)^36 - 850[(1.0085) + (1.0085)^2 + ... + (1.0085)^36] - 12200
0 = C(1.0085)^36 - 850[1.0085 - (1.0085)^37] / (1 - 1.0085) - 12200

solve for C,

C = $35,484.85

I think the working out above is kinda complicated =S
This should be a much quicker solution, i think:

A = 850 x (1-(1+0.102/12)^-36)/(0.102/12) x (1 + 0.102/12) + 12200(1+0.102/12)^-36

So you use annuities due, then add the present value of the 12200

 

[studymon]

How about this question:

A school in the Eastern suburbs is planning to set up a trust fund to make the school independent of government funding in 10 years time. THey plan to fundraise a set amount from the local parents and local community each year till then, putting the money at the end of each year in an account that will earn 8.2% p.a. compounded annually. At the end of 10 years, the school will deposit the whole balance of the fundraising account into a trust fund, which they hope will provide funds of 126,000 at the end of every year thereafter, for ever. If the trust fund will operate at 11.2% p.a. compounded annually, what is the set amount the school must raise per year over the next 10 years to carry out their plan?

ans: 76923.72

 

[studymon]

and this:

I can spend $360, 000 on a lakeside block of land and leave it untouched for two years. The only costs will be rates of $1,500 payable at the end of both years. If i can sell the block for $520,000 after two years what is the internal rate of return?

ans: 19.803%

 

[uhawww]

This is why you shouldn't leave study until the last few days and attend your PASS classes.

 

[studymon]

lol fine, =P

ahh...1 more hour to go till QMA exam !!