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Mine Essay

1046 words - 5 pages

Chapter 5 – Mathematics of Finance

5.1 – Simple Interest and Discount

Interest is the fee paid for using someone else’s money. You pay if you borrow money. You earn if you lend money.

Principal – The amount of money borrowed

The amount of interest paid depends on:
* Interest rate
* Time

Time Period | Years | Stated Rate | Decimal Form |
72 days | 72/365 | 6 % | .06 |
4 months | 4/12 | Seven and one eighth % | .07125 |
18 months | 1.5 | Half a % | .005 |

Interest can be computed two ways:
* Simple Interest
* Compound Interest

Simple Interest Formula – I = Prt where:
* I – the amount of interest
* P – the amount of principal
* r = ...view middle of the document...

See example 8.

Do problems 28, 29, 30, 36, 37, 38, 39

5.2 Compound Interest

Normally used for loans or investments greater than one year
Interest is paid (or earned) on interest

Type of Compounding | Number of periods per year - m | Annual rater | Rate per periodr/m |
Annual | 1 | .12 | .01 |
Semi-annual | 2 | .12 | .06 |
Quarterly | 4 | .12 | .03 |
Monthly | 12 | .12 | .01 |
weekly | 52 | .12 | .002308 |
Daily | 365 | .12 | .000329 |

Compound Interest Formula

A = P(1 + i)n where:

* A – the compound amount – future value
* P – the deposit – present value
* I – interest rate per period or r/m
* n – total number of compounding periods or m*t

See example 2 page 269 and example 4 page 270

Do problems 11, 17 page 277

Continuous Compounding - A = Pert

* A – the compound amount – future value
* P – the deposit – present value
* e – 2.7182818
* r – the annual rate
* t – number of years

See page307

Do problems 1 on page 309

Effective Rate (APY)

Where APY is the Annual Percentage Yield


100 invested at a simple interest rate of 7% for one year yields a maturity amount of $107, and 7/100 = .07

100 invested at 7% compounded semi-annually for one year yields a maturity amount of $107.1225 for an effective rate of 7.1225/100 = .071225, or 7.1225%

Effective Rate (APY)

re =
where re = effective rate
r = nominal or stated rate
m = number of times compounded per year

Do problem 30 on page 277

Present Value with Compound Interest

since A = P(1 + i)n then P =

See example 11 and 12 on page 275
Do problems 35, 44, 52

5.3 – Future Value of an Annuity and Sinking Funds

An annuity is a stream of equal payments made at regular intervals.

* Rent
* Car payment
* Mortgage payment
* Pension Income

Ordinary annuity – payments are made at the end of each period.

* The frequency of payments usually = the frequency of compounding
* Therefore monthly payments indicate monthly compounding i.e. mortgage payments.

Annuity due – the payments are made at the beginning of each period.


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