# 7 Using Finance Formulas

# Learn by watching

The links below will launch the video lessons in YouTube

- Simple Interest (10 minutes 36 seconds), then
**try Exercises #1-2.**

- Compound Interest (15 minutes 23 seconds), then
**try Exercises #3-4.**

- Savings Plan Formula (14 minutes 12 seconds),
**then try Exercises #5-6.**

- Loans (11 minutes 50 seconds, then
**try Exercises #7-8.**

- Choosing the Right Formula (4 minutes 8 seconds), then
**try Exercises #9-14.**

# learn by reading

## Simple Interest

Simple Interest Formula

- [latex]I=Prt[/latex]
- [latex]A=P\:+\:Prt[/latex]

*I* = interest earned

P = principal (starting value)

A = amount in account (ending balance)

r = annual interest rate (percentage must be in decimal form)

t = number of years

Exercises (Part 1): Try these!

1) You loan a sibling $200 to help them pay for a car repair. They promise to pay you back with 5% annual simple interest. Two years later, they have enough financial flexibility to pay you back. How much will they give you?

2) You spend $450 to buy a treasury bond that will mature to $500 in 5 years. What simple interest rate is your investment providing?

## Compound Interest

Compound Interest Formula

[latex]A=P\left(1+\frac{r}{n}\right)^{\left(nt\right)}[/latex]

P = principal (starting value)

A = amount in account (ending balance)

r = annual interest rate (percentage must be in decimal form)

t = number of years

n = number of compounding periods per year

Exercises (Part 2): Try these!

3) You get a small inheritance from a distant relative of $2000. You decide to put into a money market account earning 3.2% interest compounded monthly while you are saving up for a car purchase. How much much money will be in your account 4 years later?

4) You put $5000 in a stock portfolio that has traditionally earned 7% per year compounded quarterly, and then leave the account alone. How much money do you expect to have in your account after 12 years?

## Savings Plans (annuities)

Savings Plan Formula

[latex]A=\frac{d\left(\left(1+\frac{r}{n}\right)^{\left(nt\right)}-1\right)}{\left(\frac{r}{n}\right)}[/latex]

A = amount in account (ending balance)

r = annual interest rate (percentage must be in decimal form)

t = number of years

n = number of compounding periods per year

d = regular repeated deposit

Exercises (Part 3): Try these!

5) Suppose you start teaching art lessons to neighborhood children, and you make $50/week. You decide that you want to set aside $10 every week into a savings account that earns 2.7%. If you continue this for 15 years, how much money will you have in your account?

6) You want to have $1,000,000 in your retirement account when you retire in 35 years. If you find an investment portfolio that pays 6.1% interest, how much will you have to deposit every month to reach your goal?

## Loans

Loan Formula

[latex]A=\frac{d\left(1-\left(1+\frac{r}{n}\right)^{-\left(nt\right)}\right)}{\left(\frac{r}{n}\right)}[/latex]

A = amount borrowed

r = annual interest rate (percentage must be in decimal form)

t = number of years to pay off

n = number of compounding periods per year

d = regular repeated payment made

Exercises (Part 4): Try these!

7) You can afford a $1200/month mortgage. You qualify for a 30-year loan at 6.2%. How expensive of a house can you afford?

8) You want to buy a new car that costs $23,000. You qualify for a 5-year loan at 5.7%. How much will your monthly payments be?

## choosing the right formula

Exercises (Part 5): Try these!

9) You want to go on a family vacation cruise. You need to save up $4500 in the next 2 years in order to pay for the tickets. How much money will you have to invest each week into an account earning 3.5% interest in order to have enough money?

10) You decide to invest your $3000 bonus. You put it into an account earning 6.25% interest compounded monthly. How much will be in your account after 5 years?

11) You qualify for a 5.35% 6-year car loan. If you can only afford $235 monthly payments, how expensive of a car can you afford?

12) You find a treasury bond with a maturity value of $2000 in 10 years. If the bond is earning 4% simple interest each year, how much is the purchase price?

13) What would be the monthly payment on a house loan of $350,000 if you qualify for a 30-year loan at 7.3%?

14) After you retire, you’d like to be able to take out $1500 each month for the following 20 years. If your retirement account is earning 8.2% compounded monthly, how much money do you need in your account before your retire? (hint — you are taking a “loan” from yourself for these payouts).