The trustees of a college have accepted a gift of $15, but are required to deposit it in an account paying 6% per year, compounded semiannually. they may make equal withdrawals at the end of each six-month period, but the money must last 4 years. a. the amount of each withdrawal is $ (round your answer to the nearest cont.) b. if the money must last 5 years, the amount of each withdrawal is (round your answer to the nearest cont.) a. find the amount of each withdrawal. b. find the amount of each withdrawal if the money must last 5 years.

The amount of each withdrawal is $21368.46

and amount of each withdrawal if the money must last 5 years is  $17584.57

Step-by-step explanation:

given data

principal = $150000

rate = 6% per year = (6/2 )× 100  = 0.03 compound semiannually

time period = 4 year = 4× 2 = 8 half yearly

time period =  5 year = 5 × 2 = 10 half yearly

to find out

The amount of each withdrawal and he amount of each withdrawal if the money must last 5 years

solution

first we solve to find payment to each withdraw in 4 year i.e. formula

amount = principal (rate ) / 1-    ...........1

put all value rate principal time 8 half yearly in equation 1

amount = principal (rate ) / 1-  

amount = 150000 (rate ) / 1-  

amount = 150000 (0.03 ) / 1-  

amount = 21368.458324

The amount of each withdrawal is $21368.46

now we solve to find payment to each withdraw in 5 year i.e. formula

amount = principal (rate ) / 1-    ...........2

put all valye rate principal time in equation 2

amount = principal (rate ) / 1-  

amount = 150000 (rate ) / 1-  

amount = 150000 (0.03 ) / 1-  

amount = 17584.575991

amount of each withdrawal if the money must last 5 years is  $17584.57

d. $180

step-by-step explanation:

if the dimensions of the room is 9ft by 12 ft, we have the area of the floor as,

so the area of the floor is 108 square feet, converting that into square yards we get,

the cost of carpet is $15 per square yard, therefore the cost of carpet for 12 square yards is,

hence, the cost of carpet is $180.

assuming the dimensions of the room be,

15 ft by 12 ft

so, the area of the floor of that room is,

we can convert 180 square feet into square yards, we know that,

1 sq ft = 0.111 sq yard

so, 180 square feet is,

so the area of floor is 20 square yards.

now, the cost of carpet is 15 dollars per square yard, therefore the cost of carpet for 20 square yards is,

so, it will cost $300.

in geometry, parallel lines are lines in a plane which do not meet; that is, two lines in a plane that do not intersect or touch each other at any point are said to be parallel. by extension, a line and a plane, or two planes, in three-dimensional euclidean space that do not share a point are said to be parallel.