# I need help with annuties!!! (1 Viewer)

#### sez

##### New Member
I have spent hours working on this one question
If anyone can do it please show me how !

Gina and Hayen take out a loan of \$70 000 over 25 years at 8% p.a interest compunding monthly. Their repayment is \$540 per month. After 5 years of repaying the loan they make a lump sum payment of \$15 000.
How long will it now take to repay the loan?

The answer is 16 years and 10 months

Anyone who can work this one out is really smart or I am just really dumb! thanks,

sez

#### Big Willy

##### Cabra Junkie RULES
jesus! thats like a 3unit question or somthing.

I dont have much time to work out, but is this a series type question, or is it a interest type question?

Remeber, P(prinicpal) is \$70,000,

Time to pay loan is: 25 x 12 months = 300months (this doesnt take into account the lump sum of 15000)

rate is 8/100/12 (since it is compounded monthly)

So first payment would be, 540*(1+ rate), which is 540(1.00667), which equals what ever. 2nd payment would be amount owing times the rate and so on.

actually, i have a feeling this is a geometric type question...

#### sez

##### New Member
yeah that would work but

- that method would work but I think it would take ages to do because there are 300 months and that means 300 sums.
There is a quicker way and it involves some annuity formula i think.
If you can work out the quicker way your a genius!

#### Russel_c

##### New Member
Not to sure if this is the way that you do it but here it goes

Do not copy this answer as i know it is wrong and it is incomplete, this just gives you an idea....

you have to find the annuity of the first 5 years before lump payment

i is interest paid
n is period
i=0.08\12
n=5*12

A(ni)=(1-(1+i)^-n)\i
=(1-(1+o.o8)^-60)\0.08
12 12
=49.318

Present value= payment*A(ni)
=\$540*49.318
=22631.954

remaining amount to be paid= 70000-22631..954
=47368.046 here you should also minus the 15 000 that was paid as lump sum and then follow the rest of what i have done replacing with correct values

Present Value=A(ni)*payment
47368.046=A(ni)*\$540
47368.046=A(ni)
540
87.7186037=A(ni)

A(ni)=(1-(1+i)^-n)
i
87.7186037=1-(1+(0.08\12)^-n)
(0.08\12)
87.7186037*(0.08\12)=1-1.00666^-n
0.5847906913=1-1.00666^-n
0.5847906913-1=-1.00666^-n
-0.4152093087=-1.00666^-n
0.4152093087=1.00666^-n
log0.4152093087=log1.00666^-n
log0.4152093087=-n log1.00666
n= log0.4152093087
-log1.00666
=132.2848721 months (this is wrong because i didn;t take off the 15 000 that was paid)

Once you get this answer you then add it to the five years and you should have the correct answer. I

#### bex

##### Active Member
ok i dont know if this is right but i tried!!! im still working on the second part.......

first of all you gotta work out how much is left after the 5 yrs and the lump sum so....
using the future value formula... because the future value is the final amount of money at the end of an investment period...

A=?
M=540
r= 8% / 12 months
n= 5yrs x 12months/yr so... 60

your answer is \$39677.50237
minus \$15 000 lump sum
= \$24677.50237 to pay off....

AND now for the 2nd part... stay tuned!!
i ope that helped btw...

#### bex

##### Active Member
This is really hard!!!!
im thinking find in terms of 'n' but how the hell are you sposed to do that?! if you work this out can you let me know how your sposed to do it by posting the working!?
thanks!

#### airhead

##### New Member
I've been experiencing problems with annuties as well our teacher told us it was 3 unit work which leaves me with the question why dont they do it and we can do simpler stuff or not i dunno,

airhead

#### Kezza

##### New Member
its just guess and check for the second part, annoying i know but thats all we have to do for this course.

you probably wouldnt get a question that complex in an exam.

#### sar

##### New Member
I had a really hard annuity question in my paper too. I must have tried to do it five times! It was really bad :-(

#### Winston

##### Active Member
well first of all we need to find out how much of that lump sum has exactly covered
we need to know how many yrs or mths its covered

and how much that 5 yrs totaltes to the amount