Kiara opened an rrsp deposit account on december 1, 2008 with a deposit of $1,700. she added $1,700 on january 1, 2010, and $1,700 on may 1, 2012. how much is in her account on december 1, 2016 if the deposit earns 5.6% p. a. compounded monthly? select one: a. $7,242.55 b. $7,289.55 c. $7,341.64 d. $7,356.28

The total balance on December 1, 2016 is B = $7356.28

Step-by-step explanation:

I am going to call B1 the balance for the first deposit, B2 the balance for the second deposit and B3 for the third deposit.

This is a compound interest problem.

The compound interest formula is given by:

A: Amount of money(Balance)

P: Principal(Initial deposit)

r: interest rate(as a decimal value)

n: number of times that interest is compounded per unit t

t: time the money is invested or borrowed for.

First step: Balance B1 on December 1, 2016

A = amount of money =  B1

P = 1,700

r = 0.056

n = 12(compounded mothly, and t is in years)

t = 8 years

Second step: Balance B2 on December 1, 2016

A = B3

P = 1,700

r = 0.056

n = 12(compounded mothly, and t is in years)

t: From January 1, 2010 to December 1, 2016 there are 6 years and 11 months. 11 months is 0.92 of a year. So

t = 6.92

Third step: Balance B3 on December 1, 2016

A = B3

P = 1700

r = 0.056

n = 12

t: 4 years and 7 months. 7 months is 7/12 = 0.58. So t = 4.58 years.

Final step: Total balance on December 1, 2016

B = 2195.72 + 2502.39 + 2658.17

B = $7356.28

So the total balance on December 1, 2016 is B = $7356.28

answer: ratio of volume of cone (with 3 times the height and equal diameter) to volume of cylinder is 2 to 1. the value of π is not used.

step-by-step explanation:

radius is diameter/2 = 4.

area of circle is π r^2.

volume of cylinder is height × area of base = hπr^2 = 3(4^2) π = 48π cubic inches.

not knowing the formula for volume of cone, i calculate it using calculus (which is for calculating things).

volume of cone is integral 0 to h area(y) dy. area(y) is π r(y)^2. r(y) runs r to zero as y runs zero to h, r(0) = r, r(h) = 0.

r(y) = r - r/h y

area(y) = π (r - r/h y)^2 = π (r^2 - 2r^2y/h + r^2y^2/h^2) = π r^2(1-2y/h+y^2/h^2)

antiderivative area(y) = π r^2 (y-y^2/h+y^3/(3h^2))

integral 0 to h = π r^2(h-h^2/h+h^3/(3h^2) - (0)) = π r^2(h - h + h/3) = π r^2(h/3) = π/3 r^2 h

volume of this cone is π/3(4^2)18 cubic inches.

= 6 16 π = 96π cubic inches.

cone has twice the volume, 96/48.

cone height is 6 times the cylinder.

ratio of volume formula: π r^2 cancels.

cone over cylinder ratio is 6h/3 to h, 2 to 1.