A bill for $100 is purchased for $96 three months before it is due. Find: 1 The nominal rate of discount convertible quarterly earned by the purchaser 2 The annual effective rate of interest earned by the purchaser.

1. The nominal interest rate  is 16.67%

2. The effective interest rate is 4.17%

Step-by-step explanation:

1.firstly we use the information given:

face value of bill is$100 which is denoted by Fv below.

$96 is the present value Pv of the bill denoted below.

thereafter we have n the number of periods of compounding which is 1 period.

we use the following formula for this problem to find i the nominal interest rate:

then we substitute the above mentioned values.

$100 = $96 ( 1+i/m)^1 divide both sides by $96

(100/96) = 1+ i/4   then subtract both sides by 1

(100/96)- 1 = i/4

0.0416666666667 = i/4 then multiply by 4 both sides as this was compounded quarterly so four times a year then multiply by 100 for percentage.

16.67% = i which is the nominal interest rate

2.

ieffective= (1+16.67%/4)^1 - 1

ieffective = 4.17%

80π/3 or about 83.775

step-by-step explanation:

since a cone is 1/3 of a cylinder, we need to find the base's area. since area = πr^2, we get 16π. then, multiplying this by 5, we get 80π. dividing by 3, since the cone's volume is 1/3 of that of a cylinder's, we get 80π/3.

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it has the same slope and a different y-intercept

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