Question

Nina deposits $3500 into a savings account. The rate of simple interest
is 5.5%/a.
a) By how much does the amount in her account increase each year?
b) Determine the amount in her account at the end of each of the first
5 years.
c) State the total amount as the general term of a sequence.
d) Graph this sequence

Answer 1

Do you remember the formula for simple interest SI from class

Answer 2

yes I do

Answer 3

what is that

Answer 4

I=Prt

Answer 5

ok, what is the principle P

Answer 6

3500

Answer 7

the rate is 5.5% or 5.5/100 or 0.055

Answer 8

yep

Answer 9

I geted the a

Answer 10

192.5

Answer 11

Interest = 3500 * 0.055 * period

What is the period for the interest

Answer 12

Interest = 3500 * 0.055*t

t = # years

right?

Answer 13

for the part b

Answer 14

so at the end of the first year, what is the total value of the account

Answer 15

Principle + interest

Answer 16

oh ok

Answer 17

That will be your principle for the second year,

Answer 18

3692.5

Answer 19

for the 1 year

Answer 20

actually , no this will be just simple interest, a straight line, the increase in the account value will not be part of the next interest calculation right

Answer 21

You always use the same principle 3500 for any term length...
like for 5 years it is still

Interest = 3500 * 0.055 * 5

Answer 22

o it be like 962.5

Answer 23

yeah, add that to the principle, that is the amount in the account at the end of 5 years

Answer 24

but they said we have to find for the whole year like from 1 years to 5 years

Answer 25

i find the first year year and it be 369.50

Answer 26

Total amount in her account after t years will be

Total Account = 3500 + I(t)

where
I(t) = 3500*0.055*t

Answer 27

know how can we find the amount for the 2 year

Answer 28

use t = 2, 3, 4

Answer 29

Year 2

Total = 3500 + I(2)

I(2) = 3500*0.055*2 = 385

Total = 3500 + 385 = 3885

Answer 30

Same thing for t = 3 and t=4 and t = 5

Answer 31

To graph it, you want the Y axis to be the total money in the account, and the X axis to be time t in years.

Total in account = Principle + interest
y = 3500 + 3500*0.05*x

Answer 32

why u write 3500 two times

Answer 33

and what about part c

Answer 34

Because you want the total amount of money in the account, which is the principle 3500, plus the interest, which is 3500*0.55*t

Answer 35

what about part c

Answer 36

Part c,i think just wants you to write the general function for the value of the account after t years. Which is,

Total = Principle + interest

Total = 3500 + 3500*0.55*t

or factored

Total = 3500*( 1 + 0.055 * t )

Answer 37

here is the graph...

Answer 38

notice at the start, x=0, the y axis is the initial value 3500 dollars,

Answer 39

for the part c the answer given in my book is like tn= 3500+192.50

Answer 40

right, that is the same as

tn = Principle + interest

tn = 3500 + 3500*0.055*n for n=1,2,3....

Answer 41

tn - total value of account at n year

Answer 42

tn = 3500*0.055

Answer 43

192.5

Answer 44

Yes the overall general function is

Total = Principle + interest
= 3500 + 192.5*t

Answer 45

ok but where u get 3500 again

Answer 46

that is the principle amount she deposited into the account 3500 dollars

The interest at any time t in years is, 3500*0.055*t = 192.5*t

So the total amount in the account after a time t years is the sum of the initial principle 3500 and the interest 192.5*t

Total = 3500 * 192.5*t

Answer 47

If you want to graph that, let
y = total amount
x = time t in years

y = 3500 + 192.5x

Answer 48

ok thanks a lot

Answer 49

welcome, anytime