Nicolet wants to buy a new state of the art computer for r35 000. she decides to save by depositing an amount of r500 once a month into an account earning 11,32% interest per year, compounded monthly. the approximate time it will take nicolet to have r35 000 available is

54.72 months

Step-by-step explanation:

Given:

Future value = R35,000

Annuity = R500

Interest = 11.32% per year

Interest per month, r = = 0.943% = 0.00943

Let 'n' be the total time in months taken

Now,

Future value of annuity is calculated using the formula as:

on substituting the respective values, we get

or

or

1.6601 = 1.00943ⁿ

taking log both sides, we get

log(1.6601) = n × log(1.00943)

or

0.22= n × 0.00402

or

n = 54.72  months

there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!

answer:      

step-by-step explanation: