Question

A $6,000.00 principal earns 8% interest, compounded semiannually. After 35 years, what is the balance in the account
ok so do I add 8% of the balance 35 times? (Once for each year)

Answer 1

This is compound interest, and it's compounded semianually, it actually means the effective interest rate is 4% for every semi-annum, or half-year.

So, if there are 35 years, how many half-years? :D

Answer 2

70

Answer 3

That's right :)
Now, this is compound interest, so, the balance earns interest every time.

What you said, which is, adding 8% of the balance every time, is technically what we do, but that sounds rather tedious.

Here's a better way:
The balance, or accumulated value, after n-years is given by \[\Large P\left(1+ \frac{r}{m}\right)^{mn}\]
Where P is the present value, or principal
r is the compounded rate of interest
m is the number of divisions per year (in this case 2, since it's compounded semianually, or per half-year)

n is the number of years.

Just plug in, and you'll have your answer ^_^

Answer 4

n is still 35 years okay?
And don't forget that r should not be in percent, but in decimal:
8% = 0.08

Answer 5

None of the answers are in that forum though

Answer 6

P is 6000, so... we basically have
\[\Large 6000(1.04)^{70}\]

Answer 7

Were did you get 1.04?

Answer 8

\[\Large 1+ \frac{r}m\]
r = 0.08 since the rate is 8%
m is 2, since it's compounded per half-year (semianually)
So...
\[\Large 1+ \frac{0.08}2= 1+0.04=1.04\]

Answer 9

Oh

Answer 10

Is there a easier way to multiply it out
Here are the answers
a. 22,800
b. 39,600
c. 88,712
d. 93,429

Answer 11

No... I'm sure they won't make you do this if you didn't have a calculator at your disposal.
And yes, the answer is in the choices...

Answer 12

1.04^70 Do I multiply that out first?

Answer 13

Sure. It doesn't really matter... but that does seem the most logical way.. (please tell me you have a calculator)

Answer 14

Yes I do

Answer 15

then... just key in the stuff, and you'll be set ^_^

Answer 16

It will still take for ever

Answer 17

Oh... not a scientific calculator? LOL
no matter, just google 1.04^70

Answer 18

And then multiply it to the principal, 6000

Answer 19

I dotn have oen of them

Answer 20

Yeah, google also does calculating.

Answer 21

Just google 1.04^70

Answer 22

I used online calculator and it say its only 15.571618 that cant be right

Answer 23

Yes, of course, that's not it yet, you still have to multiply that to the principal, 6000, remember? :P

Answer 24

Oh yah lol

Answer 25

Its D. :)

Answer 26

That's right ^_^

Good job...

Answer 27

Thanks :)

Answer 28

Might want to keep this in mind, in case of more questions like this:
\[\Large P\left(1+ \frac{r}{m}\right)^{mn}\]


But remember, a formula can get you only so far... and not very far if you don't know what it's for ^_^

Answer 29

Can you help me with another one please
A boat cost $92,000.00 and the depreciates in value by 15% per year. How much will the boat be worth after 10 years?
a. 18,112.45
b. 78,200.00
c. 18,941.98
d. 69,000.00

Answer 30

ohh... depreciate... it's similar, except the rate is in the negative instead of positive, since the value is decreasing.
Still this formula :
\[\Large P\left(1+ \frac{r}{m}\right)^{mn}\]
But take r = -15% or -0.15
and m = 1
since it's yearly; ie; the year is not divided.

Answer 31

I am still confused

Answer 32

Sorry I just don't understnad

Answer 33

Evaluate:
P = 92000
r = -0.15
m = 1
n = 10 yrs

Answer 34

Ok so then it would be 0.925^10

Answer 35

m=1, okay? not 2.
Because this is per year, not per half-year.

Answer 36

Oh

Answer 37

So 0.85 ^ 10?

Answer 38

Yes, and when that's done, multiply that to the principal.

Answer 39

= 0.19687440434072?

Answer 40

and multiply to the original value.

Answer 41

A?