Basic Mathematics for College Students

Chapter 6 Summary and Review 585

When using the formula , the time must
be expressed in years.If the time is given in days
or months, rewrite it as a fractional part of a year.

Here are two examples:

• Since there are 365 days in a year,


• Since there are 12 months in a year,

4 months

4

12

year

4

1

3  4

1

year

1

3

year

60 days

60

365

year

5

1

 12

5

1

 73

year 

12

73

year

IPrt FINES A man borrowed $300 at 15% for 45 days to get his car out of

an impound parking garage. Find the simple interest that must be paid

on the loan.

Since there are 365 days in a year, we have

Simplify the fraction.

The time of the loan is year. To find the amount of interest, we

multiply.

This is the simple interest formula.

Write the rate ras a decimal.

Write $300 and 0.15 as fractions.

Multiply the numerators.

Multiply the denominators.

Do the division. Round to the nearest cent.

The simple interest that must be paid on the loan is $5.55.

I$5.55

I

$405

73

I

$300

1



0.15

1



9

73

I$3000.15

9

73

IPrt

P$300 r15%0.15 t

9

73

739

45 days

45

365

year 

5

1

 9

5

1

 73

year

9

73

year

Compound interestis interest earned on the
original principal and previously earned interest.

When compounding, we can calculate interest:

• annually:once a year


• semiannually:twice a year


• quarterly:four times a year


• daily:365 times a year

COMPOUND INTEREST Suppose $10,000 is deposited in an

account that earns 6.5% compounded semiannually. Find the amount

of money in an account at the end of the first year.

The word semiannuallymeans that the interest will be compounded

two times in one year. To find the amount of interest $10,000 will earn

in the first half of the year, use the simple interest formula, where tis

of a year.

Interest earned in the first half of the year:

This is the simple interest formula.

Write the rate ras a decimal.

Write $10,000 and 0.065 as fractions.

Multiply the numerators.

Multiply the denominators.

Do the division.

The interest earned in the first half of the year is $325. The original

principal and this interest now become the principal for the second

half of the year.

To find the amount of interest $10,325 will earn in the second half of

the year, use the simple interest formula, where tis again of a year. 12

$10,000$325$10,325

I$325

I

$650

2

I

$10,000

1



0.065

1



1

2

I$10,0000.065

1

2

IPrt

P$10,000 r6.5%0.065 t

1

2

12