## Archive for July, 2014

## Subset

**Subset**

Set *A *is a **subset **of set *B *(written if every element of *A *is also an element

of *B*. Set *A *is a *proper subset *(written if and .

## Present value of an Annuity

**Present value of an Annuity**

The present value *P *of an annuity of *n *payments of *R *dollars each at the end of

consecutive interest periods with interest compounded at a rate of interest *i *per

period is

## Future Value Of an Ordinary Annuity

**Future Value Of an Ordinary Annuity**

Where

*S *is the future value;

*R *is the payment;

*i *is the interest rate per period;

*n *is the number of periods.

## Sum Of Terms

**Sum Of Terms**

** **

If a geometric sequence has first term *a *and common ratio *r*, then the sum S_{n} of the first *n *terms is given by

## Present Value for Compound Interest

**Present Value for Compound Interest**

The present value of A dollars compounded at an interest rate I per period for n periods is

P = or P = .

## Effective Rate

**Effective Rate**

The effective rate corresponding to a stated rate of interest r compounded m times per years is

r_{e} =

**Example:-**

A bank pays interest of 4.9% compounded monthly. Find the effective rate.

**Solution:-**

Use the formula given above with r = .049 and m = 12. The effective rate is

r_{e } =

= .050115577 = 5.01 %

## Compound Amount

**Compound Amount**

A = P( 1 + i)^{n},

Where i = and n = mt,

**A** is the future (maturity) value;

**P** is the principal;

** r** is annual interest rate;

**m** is the number of compounding periods per year;

**t** is the number of years;

**n** is the number of compounding periods;

**i** is the interest rate per period.

Example:- Suppose 1000 is deposited for 6 years in an account paying 4.25% per year compounded annually.

**(a) Find the compound amount.**

Solution:- In the formula above, P = 1000, I = .0425, and n = 6(1) = 6.

A = P(1 + i)^{n}

A = 1000(1.0425)^{6}

Using a calculator, we get

A = 1283.68 the compound amount.

** **

**(b) Find the amount of interest earned.**

Soluion:- Subtract the initial deposit from the compound amount.

Amount of interest = 1283.68 – 1000 = 283.68

## Simple Interest Rate Find

** Simple Interest Rate Find**

**Example:-**

Carter Fenton wants to borrow 8000 from Christine O’Brien. He is willing to pay back 8380 in 6 months. What interest rate will he pay?

**Solution:-**

Use the formula for future value, with A = 8380, P = 8000, t = = .5, and solve for r.

A = P(1 + rt)

8380 = 8000(1 + .5r)

8380 = 8000 + 4000r (Distributive property)

380 = 4000r (Subtract 8000)

r = .095

Thus, the interest rate is 9.5%

## Future or Maturity Value for Simple Interest

**Future or Maturity Value for Simple Interest**

The future or maturity value A of P dollars at a simple interest rate r for t years is

A = P(1 + rt).

Example:-

A loan of 2500 to be repaid in 8 months with interest of 9.2%

Solution:-

The loan is for 8 months, or = of a year. The maturity value is

A = P( 1 + rt)

A = 2500(1 + .06133) = 2653.33

or 2653.33. (The answer is rounded to the nearest cent, as is customary in financial problems.) Of this maturity value.

2653.33 – 2500 = 153.33

Represents interest.

## Simple Interest

**Simple Interest**

I = Prt,

where p is the principal;

r is the annual interest rate;

t us the time in years.

Example:-

To bye furniture for a new apartment, Jennifer Wall borrowed 5000 at 8% simple interest for 11 months. How much interest will she pay ?

Solution:-

From the formula, I = Prt, with P = 5000, r = .08, and t = (in years). The total interest she will pay is

I = 366.67.