Calculating Compound Interest (by venaholub27)

Compound interest increases at a faster rate than simple interest because the interest is figured in more often, and is figured in to the most recent value making it a more exponential increase.*as shown in the graph below*

Calculating Compound Interest!!by: Vena Holub

Another similar interest formula is the continuous intrest formula. Where A or A(t) is the amount at time t, P is the principal or initial amount, e is the number ''e'' equaling about 2.718, r is the interest rate in the form of a decimal, and t is time in years.

Compound Interest Formula

A or A(t) is the amount A at a time t.P is the principal or initial amount started with.r is the interest rate in decimal form ex. 8% is 0.08 n is the number of times the interest is compounded per year. t is the time in YEARS!

Common Values of n:yearly/ annually n 1biannually/semi-annually n 2trimesterly n 3quarterly n 4monthly n 12weekly n 52daily n 365

The compound interest formula is usedin pre- calculus as well as everyday life. It is a way of calculating how much of something (usually money) will be present at a specific time based on factors like: the initial amount, the interest rate, the number of times the interest is compounded, and the time over which the interest is collected. Continuous interest is similar, but uses a different equation to demonstrate the value at a time, if the interest was figured in constantly at every moment.

*TIPS TO STAY ON TRACK*-don't round decimals until the last step (round to decimal place the question asks)-In a multiple step problem the more times the amount is compounded, the higher the final amount should be.-you can solve for any variable, depending on the info given in the question.

LET'S PRACTICE

1.) You invest $16,000 in an account with an interest rate of 9% for 4 years. Find the amount if the interest is compounded a. semi-annually, b. quarterly, and c. daily.A(t) = 16000 [1+ (.09/n)^n(4)a.) A(t)= 16000 [1+ (.09/2)] ^2(4) A= 16000 (1.045)^8 A= 16000 x 1.422100613 A=$22753.61b.) A(t)= 16000 [1+ (.09/4)] ^4(4) A= 16000 (1.0225)^16 A= 16000 x 1.427621457 A=$22841.94c.) A(t)= 16000 [1+ (.09/365)] ^365(4) A= 16000 (1.000246575)^1460 A= 16000 x 1.43326581 A=$22932.25

2.) Hannah can't remember how much money she put into her bank account three years ago, but she currently has $19,000 at a 12% interest rate, compounded monthly. How much money did she invest 3 years ago? Round to the 100th place. 19000= P [1+ (.12/12)]^12(3) 19000= P (1.01)^36 19000= P (1.430768784) *divide each side by 1.430768784* $13279.57 = P3.) An account with $12,300 compounds continuously for a period of 10 years. The account collects 5% interest. Calculate the amount of money after 10 years, rounded two decimal places. A(t)= 12300e^.05(10) A(t) = 12300e^.5 A(t)= 12300(1.648721271) A(5)= $20279.27

For more help and videos visit profrobbob's channel on youtube, where multiple pre calc topics are categorized and reviewed.