Sorry - another question.
For the following, I got $97,800 as an answer. Is this correct? It doesn't seem to make sense. I know I'm doing something wrong here, but what could it be?
Tula repays her father $4890 to cover a debt for a motorbike which she incurred 15 months ago, agreeing to pay 4% p.a. How much did she borrow?
Tula repays ... $4890 to cover a debt ... incurred 15 months ago, agreeing to pay 4% p.a.At the end of the first year the interest (at 4%) amounted to:
How much did she borrow?
InterestFor1Year = BORROWED x 0.04
Since this is "per annum" it is assumed that the compounding is on a yearly basis, that is the interest in added only once per year.
The amount owed at the end of the first year is
The original amount BORROWED plus the interest on that amount for 1 year:
Debt1Year = BORROWED + ( 0.04 x BORROWED )
The borrower needs to pay interest on the interest.
3 months is 1/4 year or 0.25
InterestFor3Months = Debt1Year x 0.04 x 0.25
DEBT or Total Amout repaid is $4890.
That consists of:
The original amount BORROWED
The interest on that amount for 1 year
plus the interest on that interest for 1/4 year
plus the interest on the original amount BORROWED for an additional 1/4 year.
4890 = BORROWED + (0.04 x BORROWED) + ( (1.04 x BORROWED) x 0.04 x 0.25 )
1 equation 1 unknown
4890 = BORROWED + 0.04 x BORROWED + 0.0104 x BORROWED
4890 = BORROWED ( 1 + 0.04 + 0.0104 )
4890 = BORROWED x 1.0504
You should ALWAYS check your work.
From that number BORROWED
multiply it by 1.04 (& round to the nearest penny)
multiply that amount by (1 + 0.04/4)
The final amount should be $4890.
There is really nothing simplier than using the exponentials for such problems.