3/19-20 Wed-Thursday, Compound Interest
Post date: Mar 18, 2014 9:15:26 PM
Notes:
Compounding interest is "interest on interest." It is a method of calculating interest where the interest is added to the original principle. This new value is now our principle for the next time period. In this method the interest earned in past terms can earn interest in future terms. Simple interest is a type of interest that is payed only on the original amount deposited and not on past interest payed.
Let's look at simple interest first:
A = p(1 + rt)
p= principle
r= interest rate (in decimal form)
t = time in years
Sarah started her account with $1000.00 at a rate of 8%. We looked at the total after 5 years. Find the simple interest.
A = $1000.00 (1+ (0.08)(5))
A=$1000.00 + $400 = $1,400.00
Compound interest is a little different:
A=P(1+r/n)^nt
P=original principle
r= interest rate (in decimal form)
n= number of times per year the interest is compounded
t= number of years invested
Jack started his account with $1000.00 at a rate of 8%. It was compounded twice a year, and we watched his account over a five year period. Find the compound interest.
S=($1000.00)(1+0.08/2)^(2)(5)
S=($1000.00)(1+0.04)^(10)
S=$1480.24
To calculate continously compounded interest, we will use Euler's number. Continuously compounded interest means that your principal is constantly earning interest and the interest keeps earning on the interest earned!
where,
P = principal amount (initial investment)
r = annual interest rate (as a decimal)
t = number of years
A = amount after time t
An amount of $2,340.00 is deposited in a bank paying an annual interest rate of 3.1%, compounded continuously. Find the balance after 3 years.
Use the continuous compound interest formula, A = Pe rt, with P = 2340, r = 3.1/100 = 0.031, t = 3. Recall that e stands for the Euler's number (base of the natural logarithm) which is approximately 2.7183. However, one does not have to plug this value in the formula, as the calculator has a built-in key for e. Therefore,
So, the balance after 3 years is approximately $2,568.06.
Video links that can help you:
HW: Finish off the rest of the compound interest packet, the last two pages. due Monday