Suppose you deposit a principal amount of p dollars in a bank account that pays compound interest. If the annual interest rate r (expressed as a decimal) and the bank
makes interest payments n times every year, the amount of money A you would have
after t years is given by:
A = P[1+ (r/n)]"
Find the account balance after 20 years if you started with a deposit of $1000, and the
bank was paying 4% interest compounded quarterly (4 times a year). Round your
answer to the nearest cent.

$2216.72

Step-by-step explanation:

Simply plug in your known variables into the formula:

a = 1000

r = 0.04 (4%)

n = 4

t = 20

A = 1000(1 + 0.04/4)⁴⁽²⁰⁾

A = 1000(1 + 0.01)⁸⁰

A = 1000(1.01)⁸⁰

A = 1000(2.21672)

A = 2216.72

x = central angle apc = measure of minor arc ac

the two angles x and 30 add to 180, so x+30 = 180 and x = 180-30 = 150. the measure of minor arc ac is 150 degrees.

what we need to do from here is find the circumference and then multiply it by x/360 since there are 360 degrees in a circle. in this case, x = 150, so x/360 = 150/360 = 15/36 = 5/12. the shortest distance along the curve from a to c is 5/12 of the distance around the entire circle (aka circumference)

c = circumference

c = pi*d

c = pi*24

c = 24pi

now multiply this by 5/12 to get

distance along minor arc ac = (5/12)*(circumference)

distance along minor arc ac = (5/12)*(24pi)

distance along minor arc ac = 10pi

the formula you can use is

l = (x/360)*pi*d

with

l = length of minor arc

x = central angle

d = diameter

which essentially is the steps we took though a bit differently.