Interest terms revision

First, a bit of revision:

Arithmetic progression

An arithmetic progression is any list of numbers that increase or decrease by a constant amount.

3, 6, 9, 12, 15, 18…

1, 0.5, 0, –0.5, –1…

Geometric progression

A geometric progression is any list of numbers that increase or decrease by a constant factor.

2, 4, 8, 16, 32…

10, 5, 2.5, 1.25…

Series

An arithmetic series is the sum of all the terms in an arithmetic progression.  Similarly, a geometric series is the sum of all the terms in a geometric progression.

Common Terms

Some common terms and what they mean:

Principal:  The initial amount of money invested, borrowed or lent.

Interest:  In general, a charge on the money while it is being borrowed/lent.

Rests:  The times when you stop to calculate interest.

Interest Rate:  This is a measure of how much interest must be paid on the amount of money lent/borrowed.  It is expressed in terms of a percentage of the principal that must be paid over a certain time length, usually one year.

Nominal Interest Rate:  If the interest rate is given for a period which is not a year, the nominal interest rate is the rate which would equivalently apply over one year.

Final Amount/Amount:  The final amount, or amount, is just the sum of the principal and the amount of interest built up over the time period.

Growth Factor:  The growth factor is the ratio of the final amount to the principal.

Here’s an example:

 John borrows \$1000 from the bank, at a simple interest rate of 2% per month, for a period of 10 years.  How much must he pay the bank in total to repay his loan? Solution The principal is \$1000. The interest rate is 2% per month. The nominal interest rate is 24% per year. So every year, he owes the bank 24 % of the principal in interest.  This is equal to 0.24 ´ \$1000 = \$240. This happens every year, so the total amount of interest he must pay back is 10 ´ \$240 = \$2400. The final amount he must pay back is the sum of the principal he borrowed at the start, plus all the interest he owes the bank.  This is \$1000 + \$2400 = \$3400.  So he must pay \$3400 in total back to the bank – this is the final amount. The growth factor is:

Compound interest formula

If you want to know how much money you will end up after a certain amount of time using compound interest, you can use this handy formula:

So say I wanted to find out how much money I’d have after a year, on an initial investment of \$1000, compounding monthly, at a yearly interest rate of 6%.

First thing, for this investment, interest is calculated every month, so I need to express the interest rate in terms of one month. I can do this by dividing the yearly interest rate by 12:

My principal is \$1000, and I have 12 rest periods, so I can just plug numbers into my formula now:

So after 12 months, I’ll have a total of \$1061.68 – I will have earned \$61.68 in compound interest.