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This chapter covers principles of finance. After completing this chapter students should be able to: solve financial problems that involve simple interest; solve problems involving compound interest; find the future value of an annuity; find the amount of payments to a sinking fund; find the present value of an annuity; and find an installment payment on a loan.

Chapter overview

In this chapter, you will learn to:

  1. Solve financial problems that involve simple interest.
  2. Solve problems involving compound interest.
  3. Find the future value of an annuity, and the amount of payments to a sinking fund.
  4. Find the present value of an annuity, and an installment payment on a loan.

Simple interest and discount

Section overview

In this section, you will learn to:

  1. Find simple interest.
  2. Find present value.
  3. Find discounts and proceeds.

Simple interest

It costs to borrow money. The rent one pays for the use of money is called the interest . The amount of money that is being borrowed or loaned is called the principal or present value . Simple interest is paid only on the original amount borrowed. When the money is loaned out, the person who borrows the money generally pays a fixed rate of interest on the principal for the time period he keeps the money. Although the interest rate is often specified for a year, it may be specified for a week, a month, or a quarter, etc. The credit card companies often list their charges as monthly rates, sometimes it is as high as 1.5% a month.

Simple interest

If an amount P size 12{P} {} is borrowed for a time t size 12{t} {} at an interest rate of r size 12{r} {} per time period, then the simple interest is given by

I = P r t size 12{I=P cdot r cdot t} {}

The total amount A size 12{A} {} also called the accumulated value or the future value is given by

{} A = P + I = P + Pr t size 12{A=P+I=P+"Pr"t} {}

or A = P 1 + rt size 12{A=P left (1+ ital "rt" right )} {}

Where interest rate r size 12{r} {} is expressed in decimals.

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Ursula borrows $600 for 5 months at a simple interest rate of 15% per year. Find the interest, and the total amount she is obligated to pay?

The interest is computed by multiplying the principal with the interest rate and the time.

I = Pr t size 12{I="Pr"t} {}
I = $ 6000 .15 5 12 = $ 37.50

The total amount is

A = $ 600 + $ 37.50 = $ 637.50 size 12{ matrix { A=$"600"+$"37" "." "50" {} ##=$"637" "." "50" } } {}

Incidentally, the total amount can be computed directly as

A = P 1 + rt = $ 600 1 + .15 5 / 12 = $ 600 1 + .0625 = $ 637.50 size 12{ matrix { A=P left (1+ ital "rt" right ) {} ##=$"600" left [1+ left ( "." "15" right ) left (5/"12" right ) right ] {} ##=$"600" left (1+ "." "0625" right ) {} ## =$"637" "." "50"} } {}
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Jose deposited $2500 in an account that pays 6% simple interest. How much money will he have at the end of 3 years?

The total amount or the future value is given by A = P 1 + rt size 12{A=P left (1+ ital "rt" right )} {} .

A = $ 2500 1 + .06 3 = $ 2950 size 12{ matrix { A=$"2500" left [1+ left ( "." "06" right ) left (3 right ) right ]{} ## =$"2950"} } {}
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Darnel owes a total of $3060 which includes 12% interest for the three years he borrowed the money. How much did he originally borrow?

This time we are asked to compute the principal P size 12{P} {} .

$ 3060 = P 1 + .12 3 $ 3060 = P 1.36 $ 3060 1.36 = P $ 2250 = P size 12{ matrix { $"3060"=P left [1+ left ( "." "12" right ) left (3 right ) right ]{} ## $"3060"=P left (1 "." "36" right ) {} ##{ {$"3060"} over {1 "." "36"} } =P {} ## $"2250"=P} } {}

So Darnel originally borrowed $2250.

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A Visa credit card company charges a 1.5% finance charge each month on the unpaid balance. If Martha owes $2350 and has not paid her bill for three months, how much does she owe?

Before we attempt the problem, the reader should note that in this problem the rate of finance charge is given per month and not per year.

The total amount Martha owes is the previous unpaid balance plus the finance charge.

A = $ 2350 + $ 2350 .015 3 = $ 2350 + $ 105.75 = $ 2455.75 size 12{ matrix { A=$"2350"+$"2350" left ( "." "015" right ) left (3 right ) {} ##=$"2350"+$"105" "." "75" {} ## =$"2455" "." "75"} } {}

Once again, we can compute the amount directly by using the formula A = P 1 + rt size 12{A=P left (1+ ital "rt" right )} {}

A = $ 2350 1 + .015 3 = $ 2350 1.045 = $ 2455.75 size 12{ matrix { A=$"2350" left [1+ left ( "." "015" right ) left (3 right ) right ]{} ## =$"2350" left (1 "." "045" right ) {} ##=$"2455" "." "75" } } {}
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Source:  OpenStax, Applied finite mathematics. OpenStax CNX. Jul 16, 2011 Download for free at http://cnx.org/content/col10613/1.5
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