problem of the day
DESCRIPTION
Problem of the day. When making a purchase for a big ticket item (house, car, etc.) in the near future, you might want to talk to friends and associates about the purchase to seek their:. Lesson Objective Determine the compound interest and the amount. Content Vocabulary. compound interest. - PowerPoint PPT PresentationTRANSCRIPT
Problem of the day..
• When making a purchase for a big ticket item (house, car, etc.) in the near future, you might want to talk to friends and associates about the purchase to seek their:
compound interestInterest earned not only on the original principal but also on the interest earned during previous interest periods, earning interest on interest.
Lesson Objective Determine the compound interest and the amount.
Content Vocabulary
compound interest
Remember “Time Value of Money”
• The longer you keep money in an interest bearing account, the more money you will make
• Compounding can be done different ways, and the more frequently interest compounds, the faster it grows.
• See example on the next slide:
Compounding Interest Over Time
5 years 10 years
Money under mattress $1,000 $1,000
Annual Compounding5%
$1,276 $1,629
Monthly Compounding5%
$1,283 $1,647
Daily Compounding5%
$1,284 $1,649
Item Average Yearly Expense
Future Value
Eating lunch out 5 days per week at a cost of $5-$10 each time
$1,300.00-$2,600.00 $55,140.60 - $110,281.21
Daily candy bar ($1.00) $365.00 $15,481.78
Monthly gym membership at $38.00
$456.00 $19,341.63
Monthly hair cut at $25.00 per month
$300.00 $12,724.75
Calculated for an 18 year old person investing at 8% until age 65.
Quarterly: A period of time out of one year. Each year has 4 quarters.
One quarter is how many months?
3 months
Example:You open a savings account and deposit $1,000. Your bank advertises a 6% annual interest rate that is compounded quarterly (that means you calculate interest every 3 months and add it to the principal). What is the amount in the account at the end of one year? How much is the compound interest?
1. Find the interest at the end of the 1st quarter by using I = P x R x T
$______ x _____ x _____ = $________
2. Find the Amount at the end of the 1st quarter (A = P + I) $________ + $________ = $_________
3. Find the interest at the end of the 2nd quarter using the “new” Principal.
$_________ x _________ x ________ = ______
4. Find the Amount at the end of the 2nd quarter$______ + $_______= $_________
5. Find the interest at the end of the 3rd quarter using the “new” Principal.
$________ x _______ x _________ = ___________ (round)
= ___________(interest)
6. Find the Amount at the end of the 3rd quarter$_________ + $_______ = $___________
7. Find the interest at the end of the 4th quarter using the “new” Principal.
$________ x _____ x ______= $_______ round $________
8. Find the Amount at the end of the 3rd quarter$__________ + $________ = $____________
This is how much money is in the bank at the end of the year
How much total interest did you earn?
• $15.00 (1st quarter) + $15.23 (2nd quarter) + $15.45 (3rd quarter) + $15.69 (4th quarter) = $61.37
Challenge Problem:
$10,000 investment earned interest at 4.5% compounded quarterly for 1 year and 5.5% compounded quarterly for the next year. What is the amount in the account at the end of 2 years?
How many different compounding periods are there? ____
Setup of the first year:Setup of the second year:
Challenge: Hint
8 periods
10,000 x .045 x ¼ , calculate four times add interest to principal after each period
10,000 x .055 x ¼ , calculate four times add interest to principal after each period
www.marsbank.com
savings calculator
p. 227 Answer keys
9. $1,200 x .06 x 3/12 = $18$1,200 + $18 = $1,218$1,218 x .06 x 3/12 = $18.27$1,218 + $18.27 = $1236.27 (a.)$18 + $18.27 = $36.27 (b.)
12. $860 x .055 x 6/12 = $23.65$860 + $23.65 = $883.65$883.65 x .055 x 6/12 = $24.30$883.65 + $24.30 = $907.95 (a.)$23.65 + $24.30 = $47.95 (b.)
14.$9,544 x .0525 x 1/12 = $41.755 ($41.76)$9,544 + $41.76 = $9,585.76$9,585.76 x .0525 x 1/12 = $41.94$9,585.76 + $41.94 = $9,627.70$9,627.70 x .0525 x 1/12 = $42.12$9,627.70 + $42.12 = $9669.82$9669.82 x .0525 x 1/12 = $42.31$9669.82 + $42.31 = $9,712.13 (a.)
$41.76 + $41.94 + $42.12 + $42.31 = $168.13
#16– Page 2272000 dollars @ 6% compounded semiannually ( 2x)
I= P x R x TJuly 1st - I= 2000 x .06 x 6/12 = 60 A = I + PA = 60 + 2000 = 2060Add: 2000 dollarsJanuary 1 – I = (2060 + 2000) x .06 x 6/12 = 4060 x .06 x 6/12 = 121.80Amount = 4060 + 121.80 = 4181.80
Finally, compound interest = 181.80