Hence, if either of the Quantities be given on the line Bc, a portion representing the other may be found

PROBLEMS

For Interest we have in all cases

y: x

377

The Equation to a straight line passing through the origin at an angle of 45°

For Banking Discount,

y'

To find the Amount of a given Sum in any Time at

Compound Banking Discount

6. Let R denote the amount of £1 with its Interest for

=1+r

amount of £1 with its Discount for one year

=

1

Then PR'

=

amount of P in one year

PR'2

The amount of PR' in one year is PR'R' ... PR'2 = = amount of P in two years at Comp. Discount PR'3 amount

SO

To find in what Time a Sum of Money will double itself at Compound Banking Discount

Hence a sum of Money will double itself at 5 per cent. :

At Simple Interest in 20 years

Discount 19 99

Compound Interest

14.206609 years

Discount 13:51

8. The formulæ for the Amount of a Sum in any given Time at Simple Interest and Banking Discount: and Compound Interest and Banking Discount are―

P ( 1 + nr

)

These four formulæ will enable us to solve any Problems in the subject

To find the Difference in Profit at the end of the Year between discounting one Bill for £1,000 at twelve months, and discounting four Bills of £1,000 at three months in succession, at 5 per cent. Compound Discount

To find the Profit on discounting at more frequent intervals than a year

2

10. Suppose the interval is six months, then will be the Discount of £1 for year

At Compound Discount the amount of P in n years is P (1 + 1)":

2

)2": because the amount is the same as if the number

of years were 2n and the Discount on £1 for one year

2

So for four months, or three intervals, the amount is—