Solving Finance Problems - College Algebra

Cypress College Math Department – CCMR Notes Solving Finance Problems – College Algebra, Page 1 of 13

Solving Finance Problems – College Algebra

Objective 1: Simple Interest Formula

Interest rate as a percentage

Interest rate as a decimal

10%

8.4%

0.3%

Time in Months Time in Years

15 months

6 months

8 months

Example: Find the interest earned if $400 is invested at a 5% simple interest rate for 18 months.

Example: What principal would need to be invested at a 4% simple interest rate if you will earn $28 interest in 4

months.

interest = Prt P= principal

r = annual simple interest rate

t = time in years


Example: Find the simple interest rate needed to earn $18 interest, if $400 is invested for 20 months.

Example: How long would it take to earn $27.75 in interest, if $370 is invested at a 3% simple interest rate.

Example: Find the future value if $220 is invested at a simple interest rate of 2% for 6 months.

Example: Find the present value if the future value is $460, the simple interest rate is 5% and the time is 3 years.

Example: Find the simple interest rate if $495 is invested for 4 years, and it grows to $520.

1

Amount = Principal+interest

A= P+Prt

A= P +rt

,

,

A amount also called the future value

P= principal also called the present value

r = annual simple interest rate

t = time in years

A= P+Prt 1A= P +rt


Example: How long would it take for $200 to grow to $250 at a simple interest rate of 3%?

Example: Find the time it would take for each of the following.

A P r

$448 $400 4%

$817.20 $720 6%

$1161.05 $1100 7.4%

Example: Solve for each of the variables in each of our simple interest formulas:

i = Prt, A= P+Prt, and A= P 1+rt


Pause the video to try this one on your own, then restart when you are ready to check your answer.

Extra Practice

Questions

1. What principal would need to be invested at a 4% simple interest rate if you will earn $70 interest in 5 months.

2. Find the simple interest rate if $725 is invested for 2.5 years, and it grows to $770.31.

Restart when you are ready to check your answers.

Objective 2: General Formula for Compound Interest Year Principal Interest Amount of money at the end


Example: Find the number of times compounded per year (m or n) if interest is compounded:

a. Annually

b. Semiannually

c. Quarterly

d. Monthly

e. Daily

Example: If the interest rate per compounding period is 2%, where interest is compounded monthly, what is the annual

interest rate?

Example: If the interest rate per compounding period is 0.05%, where interest is compounded daily, what is the annual

interest rate?

1

ntr

A= P +n

,

,



r = annual interest rate

n or m number of times compounded per year

t = time in years

1

mtr

A= P +m

For compound interest, the interest is calculated

every term, then added to the principal. So, the

principal grows each term.

annual interest rateinterest rate per compounding period =

number of times compounded per year


Example: If the annual interest rate is 4.2%, and interest is compounded semiannually, what is the interest rate per

compounding period?

Example: If the annual interest rate is 7.1%, and interest is compounded quarterly, what is the interest rate per

compounding period?

Example: Find the future value if $3250 is invested at 6% compounded monthly for 3 years.

Example: What would the present value need to be, if the money in the account grew to $4230 after 4 years, and the

account pays 3.5% compounded daily?


Example: It is very common to be given the future value and asked for the present value for compound interest

problems. Solve the compound interest formula for P, to make these problems easier.


Extra Practice

Questions

1. If the interest rate per compounding period is 1.3%, where interest is compounded monthly, what is the

annual interest rate?

2. If the annual interest rate is 6.5%, and interest is compounded semiannually, what is the interest rate per

compounding period?


3. What would the present value need to be, if the money in the account grew to $595.11 after 3 years, and

the account pays 4.2% compounded quarterly?

4. Find the future value if $5600 is invested at 3.5% compounded monthly for 7 years.


Objective 3: Formula for Interest Compounded Continuously

Example: $2780 is invested at 5% compounded continuously. How much will be in the account after 20 months?

rtA= Pe ,

,



r = annual interest rate

t = time in years


Example: Find the present value if the account pays 3% compounded continuously and the amount in the account after

7 years is $10,017.47.

Example: It is very common to be given the future value and asked for the present value for compound interest

problems. Solve the continuously compounded interest formula for P, to make these problems easier.


Extra Practice

Questions

1. $245 is invested at 4.3% compounded continuously. How much will be in the account after 5 years?


2. Find the present value if the account pays 8.1% compounded continuously and the amount in the account after

2 years is $1175.86.


Objective 4: Solve for Time in an Interest Problem Example: How long will it take $5025 to grow to $6194.38, if the account pays 3% compounded quarterly?

Example: How long will it take $300 to grow to $381.37, if the account pays 4.8% compounded continuously?



Extra Practice

Questions

1. How long will it take $731 to grow to $927.64, if the account pays 4% compounded monthly?

2. How long will it take $800 to grow to $838.78, if the account pays 7.1% compounded continuously?



Objective 5: Doubling Time Example: How long will it take $3500 to double, at 5% compounded quarterly?

Example: How long will it take money to double at 4.3% compounded daily?

Example: How long will it take money to double at 6% compounded continuously?



Extra Practice

1. How long will it take $3000 to double, at 4% compounded semiannually?

2. How long will it take money to double at 5% compounded monthly?

3. How long will it take money to double at 6.2% compounded continuously?


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Solving Finance Problems - College Algebra