Math Is Fun Forum

natashabaker

Member

Registered: 2007-05-25

Posts: 10

Business maths. Stuck :(

hey guys i need help with this question our teacher said it will be a similar one to the question on our test

here it is

The Smith's bought a new car priced at $34,800 and paid a deposit of $5000 cash. They borrowed the balance of the purchase price at simple interest. They then agreed to repay the loan, plus interest, in equal monthly payments of $900 over four years.

A. Calculate.
i. the total amount of interest to be repaid over the term of this loan.

ii. The annual simple interest rate charged on this loan correct to two decimal places.

iii.The effective rate of interest that they are paying on this contract, correct to one decimal place.

B. The value of this car was depreciated using a reducing balance method at a rate of 15% per year.
i. Calculate to the nearest dollar, the depreciated value of the car after three years

ii. Calculate to two decimal places, the annual percentage rate of depreciation that would reduce the value of the car from $34800 to $20000 in three years.

thank you much help will be appreciated

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: Business maths. Stuck :(

I looked up "simple interest" on google with:
"define: simple interest", and I learned that:
The interest payment is based only on the original principal and not unpaid interest.
So that makes it WAY easier to do the problem because you
don't have to go around and around in circles for 4 times 12 months minus 1, the last month.
So there are 48 months you pay.
$900 times 48 is about 45grand.
$34900 minus 5000 is 29900, and 45grand is about 15grand above 29900.
So 45 divided by 30grand is about 150% or 3/2, so that gives you your percentage,
probably 50% interest, roughly speaking.

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igloo myrtilles fourmis

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: Business maths. Stuck :(

For Aiii, you have to take a ROOT of the 150% number.
Like if you want effective ANNUAL rate, then square root 150% twice, which
takes the fourth root.
But if you want the effective MONTHLY rate, then you
have to take the 48th root of about 150%.
This is 150% up (1/48) on calculator.
UP Power means x up little y on calculator button.
So you want a number like 102% or 103% or 101% or 100.5% or something,
that when you multiply it by itself 47times (48total multiplied), then
you get 3/2 about or 1.5.
So 1.008 is just a guess...
Calculator time...
1.00848 is better I guess.
And my calculator says y up x, not x up y for the power function.
Use parenthesis to hold the 1 divided by 48 or 1 divided by 4 for annual).

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igloo myrtilles fourmis

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: Business maths. Stuck :(

Now Bii is a totally cool one.
348/200 is about 7/4 or about 10/6 or about 1.73 or something or the square root of 3 about.
Now take the cube root of this proportional (multiplicative) change.
Like WHAT times WHAT times WHAT equals 1.74 or so.
Use calculator.  1.74 up (1/3) would be about 1.22 or so, so then
1/1.22 is the reciprocal of that, or about 0.81 maybe, and 81 is 19% less than 100.
So answer would be about 19% cheaper every year on the car, approximately!!
(actual answer is 16.85% on calculator each year, but round that up to a 6.)

Note also that you can do the cube root of 200/348, then you don't have to
take the reciprocal because you get number between 0 and 1, so then you
can see how far below 1 you are to get your reducing percentage.

Last edited by John E. Franklin (2007-09-16 18:16:18)

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igloo myrtilles fourmis

natashabaker

Member

Registered: 2007-05-25

Posts: 10

Re: Business maths. Stuck :(

thank you for the quick replys and the help i understand what your saying any other info would be grand aswell thanks

Last edited by natashabaker (2007-09-16 19:15:14)