Day 6 Interst conmpounded annually and continuously.notebook
October 28, 2014
Do Now:
How much would $1,200 earn in three years using the simple interest formula, at a rate of 6%?
What would the new balance be?
Oct 17­8:24 AM
Day 6: Compound Interest
~Annually and Continuously~
Oct 17­8:19 AM
1
Day 6 Interst conmpounded annually and continuously.notebook
October 28, 2014
Oct 17­8:23 AM
yearly compound formula: A = P(1+r)t The more often money compounds, the more money you earn.
There is a formula the compounds continuously:
A = Pert
where e ≈ 2.71828182845904... or use e ≈ 2.72
Remember:
A = Final Amount
P = Principle
r = interest rate as a decimal
t = time in years
Oct 17­8:17 AM
2
Day 6 Interst conmpounded annually and continuously.notebook
October 28, 2014
Practicing Interest Earnings Problems
Remember: Interest rate % must be changed to a
decimal by moving decimal place two places!!!
When Joseph was born, his grandpa put $600 in a savings
account for him earning 1.6% interest annually. At five years old,
Joseph parents will use that money to buy him a special birthday
present. Using the formula for interest compounded annually
A = P(1 + r) t calculate the final amount Joseph will have in his
account. Sep 14­3:20 AM
Practicing Interest Earnings Problems
Remember: Interest rate % must be changed to a
decimal by moving decimal place two places!!!
When Joseph was born, his grandpa put $600 in a savings
account for him earning 1.6% interest continuously. At five
years old, Joseph parents will use that money to buy him a
special birthday present. Using the formula for interest
compounded continuously A = Pert calculate the final amount
Joseph will have in his account. Compare both final amounts, what do you notice?
Oct 17­8:39 AM
3
Day 6 Interst conmpounded annually and continuously.notebook
October 28, 2014
P= $100 r= 5% t = 10 years
Remember: e ≈ 2.72 Must be memorized!!!
A = P(1 + r)
t
vs. A = Pert
Difference?
Significant?
Sep 9­4:46 AM
PRACTICE the 2 types of interest earnings formulas we used.
1) Use A = P(1+r)t
principle: $2000
rate: 1.3%
time: 40 years
2) Use A = Pert
principle: $2000
rate: 1.3%
time 40 years
Sep 14­3:50 AM
4
Day 6 Interst conmpounded annually and continuously.notebook
October 28, 2014
3) principle: $2000
rate: 0.65%
time: 15 years
Use A = P(1+r)t
Use A = Pert
4) principle: $900
rate: 1.29%
time: 25 years
Use A = P(1+r)t
Use A = Pert
Sep 14­3:25 AM
Exit Ticket Day 6:
Tomorrow you will work independently on all interest formulas, it will be collected and graded
Oct 17­10:36 AM
5
Day 6 Interst conmpounded annually and continuously.notebook
October 28, 2014
But when using formula, use "e" in the calculator
5) principle: $3000
rate: .25%
time: 8 years
6) principle: $400
rate: 3%
time: 12 years
Oct 10­2:27 PM
7) principle: $200
rate: 1.60%
time: 30 years
8) principle: $750
rate: .10%
time: 15 years
9) principle: $1000
rate: 0.10%
time: 20 years
Oct 10­2:27 PM
6
Day 6 Interst conmpounded annually and continuously.notebook
October 28, 2014
EXIT TICKET
principle: $5200
rate: 0.07%
time: 10 years
A = Pert
A = P(1 + r)t
Sep 14­3:25 AM
7