Question

Zaineb is deciding whether to buy a stereo at $695 plus GST and PST (15%) now, or to invest the money to buy the stereo in a year. Her account pays 7.35% per annum, compounded monthly. If she can buy the stereo at the same price next year, how much would she save by investing the money?

Answer 1

The answer is $60.76 but I don't know how..

Answer 2

I tried P as the Principle invested: 695 x 0.30 = 208.50, i, as the interest rate per compounding period = 7.35% /100 = 0.0735/12 = 0.006125 and n, number of compounding periods = 1(12).

P = 695(0.30)-208.50
i = 0.0735/12 = 0.006125
n = 12

A = P(1+i)^n
= 695(1 + 0.006125)^12
= 224.35

Interest earned = Amount - Principle
= 224.35 - 208.8 (is it?)
= 15.55

Answer 3

total cost of the stereo is (695)*.15 + 695 = 799.25

Answer 4

I got it wrong D;

Answer 5

I was going to work it through with you but it seems to me you are using the wrong number for the principle :D

Answer 6

Ok so she is going to invest 799.25 cents thus we use the compound interest formula

A = P(1 + (r/n))^(nt)

A is what we are looking for
P = 799.25
r = 7.35%/100 = 0.0735
n = 12
t = 12

Answer 7

ohh.. D:

Answer 8

how did you know when to use the compound interest formula? What was my formula called? o.o

Answer 9

Maybe take a break :d seems like you have the math down just comprehension is a bit off :P

Answer 10

your formula is the same as mine you are just using i to denote (r/n)

Answer 11

ohhhh, i see.

Answer 12

but it should be to the power of nt not just n

Answer 13

yeah I have it on my notes too but my math textbook had me use that formula. Oh, i see.

Answer 14

the time is also 12? not 1?

Answer 15

because I multiplied 1 with 12, instead of 12 by 12.

Answer 16

t = 1

Answer 17

oh, and n = 12.

Answer 18

the n is denoting that there are 12 compounds in a year and the t is stating that it is 1 year

Answer 19

if you don't mind me asking what are compounds? .. :$ oh, i see.

Answer 20

So you wouldn't really see the t as an exponent in this question because it is 1

Answer 21

oh, okay.

Answer 22

1 compound is when the interest is added to the total amount of money

Answer 23

invested

Answer 24

so the amount you invested is increased by 7.35% every compound

Answer 25

ohh, i see.

Answer 26

if the interest was 15% on 695 after 1 compound your annual or A would equal 799.25

Answer 27

ohhh, okay.

Answer 28

2 compounds it would be 799.25(.15) + 799.25 = A
but yeah did you get the right answer?

Answer 29

it's 919.14

Answer 30

and I subtract that from?

Answer 31

You would subtract it from the total cost of the stereo 799.25 doesn't seem right

Answer 32

huh?

Answer 33

Ok so she is going to invest 799.25 cents thus we use the compound interest formula

A = P(1 + (r/n))^(nt)
A is what we are looking for
P = 799.25
r = 7.35%/100 = 0.0735
n = 12
t = 1

799.25(1+(0.0735/12))^(12*1)
=860.01
860.01-799.25 = 60.76

Answer 34

ohh.. i forgot to do the power.

Answer 35

Well good luck I hope I was a help

Answer 36

thank you!!