FoM 12

1

1.3 Compound Interest and Future Value Calculations

So far we have discussed the difference between _____________ and ___________ interest and have done simple calculations involving tables.

Example: $23000 is invested in an account that earns 13.6% annually, compounded semi-annually. Find the present value of the investment after 5 years:

What if we want to __________ the future value of an investment __________ compounding periods in the future?

i.e. term of 50 years compounding monthly?

As you can see this is not a practical way to work with compound interest…

The future value of an investment earning compound interest is given by the following formula:

𝑨 = 𝑷(𝟏 + 𝒊)𝒏

Where:

• A = Future Value • P = Principal • 𝑖 = Interest Rate per compounding period • 𝑛 = number of compounding periods

Simple Compound

gunnerFuture

Year FvOF

f HI icomp period 2 or 31,958.33

3 34,131 So

3 s 36,452.44 IS 44,405 874 38,931.214.5 41,578.535 44,405.87

project Many

Year frIMonth

2monthi L

Goomonth

PreCalculus 12

2

Example: Emma sells her old FoM 12 notes online and makes $50,000 off of it (they are very sought after). She chooses to invest it in a retirement account for 50 years while she works. The investment that she chose pays 12% interest compounded semi-annually. How much money will she have for her retirement after 50 years?

Example: Kaelie gets a scholarship for $50,000 but she only needs half of it for her tuition and plans to work part-time to cover the rest of her living expenses. She decides to invest $25,000 in an account that will pay her 8% interest compounded quarterly. Determine the future value after:

i) 4 years

ii) 10 years

iii) 15 years

iv) 20 years

v) 39 years

P so ooo A p it in

too12t Int 0.12 50,000 11 0.06

too

1 0.06 SO ooo 1.06

SO ooo 339.3so yearsA 16,965,104.18n 100comp periods

f 25 oooA PCiti

D It 2sooo I to.az I 27 0 0225ooo 1.02 t

A134,319.64

n 40 A 2sooo Ito.ozo

A sS2oo99

n 60 A 2500011.02

A ts82.025TT

A 25000 1.028

n 80

py.sk2l 88S

9TA2Soooi.ozYS6n156A.esS48,992

PreCalculus 12

3

Example: Timmy and Tommy each invest $10,000 in an account that pays 10% annually. Timmy’s investment compounds annually, while Tommy’s investment compounds monthly. Compare the future value of their investments after 10 years.

The Rule of 72 is a simple formula used to estimate the _________ required for an investment to ___________. To use the rule, divide the number 72 by your annual ____________ __________. This will be approximately how many years are required to double your money

Example:

Wyatt has $500 to invest in an account that pays 6% annually compounded monthly. He needs $1000 to buy textbooks for his first year university courses.

a) Estimate the length of time required for his investments to double.

b) To the nearest year, calculate how much his investments will be worth after this period of time.

Assignment: WB P. 11 # 1-13

P 10,000 10 years10 annual int

I ti Em It.o.sitoooo i to 1

ooo i Yo i 10 peryear toooo 1.0083

q.is q i 00083PermonthA.es2fgf3 zy

timedouble Interest rate

i Gi per year 7 12 12years.vnhedoubleshis

p soo A p Iti144

c 0.06 annually I 500 11 0.005

0.005monthly soo t.ws m

Al025a38T1 144comp per