Download 3.6 Finance Math Interest Compounded Annually A = P(1 + r)n

December 13, 2011
3.6 Finance Math
Interest Compounded Annually
A = P(1 + r)n
Interest Compounded k Times per Year
r
A=P 1+
k
kt
Interest Compounded Continuously
A = Pert
December 13, 2011
1. Mike has $600 to invest at 8% annual interest
compounded monthly. How long will it take for his
investment to grow to $2400?
December 13, 2011
2. Sue invests $200 at 7% annual interest
compounded continuously. Find the value of her
investment at the end of each of the years 1, 2, ... , 7.
December 13, 2011
Annual Percentage Yield (APY) the percentage rate
that, compounded annually, would yield the same return
as the given interest rate with the given compounded
period.
Tom invests $2000 with Key Bank at 5.15% annual interest
compounded quarterly. What is the equivalent APY?
December 13, 2011
annuity: sequence of equal periodic payments
ordinary: deposits are made at the end of each
period at the same time the interest is posted in the
account
Future Value of an annuity, consisting of n equal
periodic payments of R dollars at an interest rate of i
per compounding period (payment interval) is:
FV = R
r
k
kt
(1 + ) - 1
r
k
December 13, 2011
3. At the end of each quarter, Emily makes a $400
payment into the Smithville Financial Fund. If her
investments earn 7.75% annual interest compounded
quarterly, what will be the value of Emily's annuity in
25 yrs?
December 13, 2011
Present Value of an Annuity consisting of n equal
payments of R dollars earning an interest rate i per
period (payment interval) is:
PV = R
1 - (1+ )-kt
r
k
r
k
Cindy purchases a new car for $19,000. What are the
monthly payments for a 3-year loan with a $3000 down
payment if the annual interest rate (APR) is 3.1%