Expert: Sherry Wallin - 10/17/2011

Question
QUESTION: Rent 800
Food 240
Electricity 100
Gas bottles 100
Petrol 300
Luxury weekend cafes’…etc approx. 200

Wifes income: 2600 per fortnight
My income: 4000 per month.

Currently we have 10k saved up and $4k in our everyday spending.
However as of October 21 we will be paying $600 into a personal loan which has 12000 owing at 16% per anum floating interest.

My question is therefore, will we still be able to save and pay off the loan within the next 4 months.

ANSWER: A.

800 + 240 + 100 + 100 + 300 + 200 = 1740 in debt monthly with 2600(2) + 4000 = 9200 monthly income
in 4 months time your debt will be 4(1740) = 6960 and your income 4(9200) = 36800
The difference is 36800 - 9200 = 27600 which is certainly more than the 12000 owing even at 16% per annum which results in 4/12 of a year thus 1/3 of a year. I = Prt = 12000(.16)(.33) = 633.60 and add that to the 12000 for a total of 12633.60. There is plenty of money to pay off 12633.60 with 36800. You never say how often you are to be paying the 600 into the personal loan.

There seems to be some crucial information missing. A floating loan is a loan that is adjustable according to the economy and it is usually compounded which I have not done but it wouldn't make a big enough difference in answering this question.

Math Prof

---------- FOLLOW-UP ----------

QUESTION: Pay $600 weekly begining 21 October.

ANSWER: This new info makes no sense. In 4 months there are approx 17-18 weeks and suppose it is 18 then 18(600) = 10800 so in 4 months paying $600 week you will not pay off  $12,000. Of course if you use some of your checking account money or savings in addition to the $600 a week there is plenty of money to pay it off in the 4 months time.

Math Prof

---------- FOLLOW-UP ----------

QUESTION: Hi there,

Perhaps I wasn't very clear:

Combined monthly income for my wife and me is 6590 for the month.

Hence I was looking at from Oct 19 paying $600 weekly and I'd like to know what the balance of the loan is going to be at end of January 31 baring in mind that the interest on the loan is calculated at 16.0% per anum, current balance is $13,139.38.

If you could help with regards to how much I would be able to pay off with the above information it would be helpful.

common other expenses include:
Rent fortnightly at $800
Food 240 fortnightly
Electricity 100 fortnightly
Gas bottles 100 montly
Petrol 300 monthly
Luxury weekend cafes’…etc approx: 50 fortnightly

Answer
a fortnight is 2 weeks or 14 days and you said your wife makes $2640 in a fortnight which means she makes at least 2(2600) = $5200 in a month. You say your monthly income is $4000 thus your combined monthly income is $9200. Now you are saying our combined monthly income is $6590, that is a BIG difference.

Is the interest that you are referring to compounded or not? And if it is compounded, how often? daily, weekly, monthly, bi-weekly, bi-monthly??
Using fortnight for rent then your monthly rent is 1600 and food 480 and electricity 200 and gas bottles 100, petrol 300, and luxuries 100 monthly for a combined total of 2780. Take your monthly income - expenses and you have 9200-2780 = 6420 to be spent or saved monthly...
You have roughly 15 weekly payments to be made at $600 so that is $9000. This tells me you will owe at least $4139.38 come January 31...now to calculate interest on the balance after each payment would go something like this:

Assuming a sort of compounded simple interest in that you are doing simple interest on the amount until the next weekly payment your interest rate per week is .16/52 = .00307692308 or about .0031 as an interest rate each week
13139.38 x (.16/52) = $4.02 or 13139.38 x .0031 = $4.07 which you see is about a nickel difference each week. So if we are going to err let's do it on the high side and use .0031

at the end of week 1 you owe 13139.38 + 4.07 - 600 = 12543.45
at the end of week 2 you owe 12543.45 + 3.89 - 600 = 11982.33
...
you have the original balance plus the interest on that balance minus your 600 payment each week for 15 weeks.
You could let 13139.38 = P0 then you have P0 + P0(.0031) - 600 = P1 => P0(1+.0031) - 600 = P1 => 1.0031(P0) - 600 = P1
P1 + P1(.0031) -  600 = P1(1.0031) - 600 => P0(1.0031) - 600](1.0031) - 600 = P2
...
P0(1.0031)^17 -600[(1.0031)^16+(1.0031)^15+( 1.0031)^14+(1.0031)^13 +(1.0031)^12+(1.0031)^11+ (1.0031)^10+(1.0031)^9 +(1.0031)^8+(1.0031)^7 +(1.0031)^6+(1.0031)^5+ (1.0031)^4+(1.0031)3 + 1.0031)^2+(1.0031)1] - 600 = amount owed after making the 16th payment.

You calculate it this will tell you how much was paid and also calculate the interest paid as well...

I come up with a balance owing of $3392.34 after making the 16th payment

Math Prof