Suppose you want to have $6 for retirement in 30 years. your account earns 9% interest compounded monthly. a) how much would you need to deposit in the account each month? b) how much interest will you earn?

a) $327.74

b) $482,021.47

Step-by-step explanation:

This sort of question is best answered using a financial calculator to compute the payment required for a particular future value. The amount of the payment will depend on whether it is deposited at the beginning of the month, or at the end. Here, we have assumed it is deposited at the end of the month.

a) The payment amount required is $327.74. (It is this amount divided by 1.0075 if deposited at the beginning of the month.)

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b) Since this payment amount is rounded up from the calculated value, the account balance will exceed $600,000 by a small amount (about $7.87). So, the interest earned will be $600,007.87 less the amount of 360 payments, $117,986.40. That interest amount is $482,021.47.

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.

(sin 42)/31. = sinx)/37

sinx = 37 (sin42)/31

= 37× 0.66/31 = 0.787

x= 51.9

other angle opposite to y = 180-51.9-42

= 180- 93.9 =86.1

so

sin42)/31 = sin 86.1)/y

0.021 = 0.997 /y

y= 0.997/0.021 =47.47