Question

a regular saving of $500 is made into a sinking fund at the start of each year for 10 years. Determine the value of the fund at the end of the tenth year on the assumption that the rate of interest is
A) 11% compounded annually
b) 10% compounded continously

Answer 1

How far have you gotten? Does it matter that it's a "Sinking Fund" or is any old accumulation sufficient?

Answer 2

the chapter is geometric series

Answer 3

Okay, how do we find a geometric series?

Answer 4

a(r^n-2)/(r-1) right?

Answer 5

If you built it, you will understand it.

Let's try 11% annual
i = 0.11
r = 1+i = 111

t = 10: 500
t = 9: 500*r
t = 8: 500*r^2
...
t = 1: 500*r^9

Add those all up and see what you get.

Answer 6

for annual
500(1+11/100)^10=1419.7

Answer 7

so i do 500(1.11^10-1/1.11-1)

Answer 8

?? You just accumulated 10 payments of $500 and only had $1419 at the end? I hope not.

Did you add up the payments?

500 + 500*r + 500*r^2 + ... + 500*r^9 = What?

Answer 9

500(1.11^10-1/1.11-1

Answer 10

500(1.11^10-1/1.11-1=8361

Answer 11

Now we're talking!

What's your plan for the continuous interest?

Answer 12

it is correct?^^

Answer 13

11% Annual - 8361.0044821

Answer 14

11%=8361 right? no -

Answer 15

it 11%annual=8361 right?
not 11%-8361

Answer 16

Not sure what you are asking. I'll be horribly clear.

Determine the value of the fund at the end of the tenth year on the assumption that the rate of interest is

A) 11% compounded annually

Answer: $8,361.00

Answer 17

Off to the continuous interest. How shall we tackle that one?

Answer 18

i am sorry yes but you 11- 8361 i am tellyouin for 11% annual =8631

Answer 19

Okay, now what is different about continuous interest?

Answer 20

how we can do conitnuous ?

Answer 21

Barely different. Rather that \(500(1.11)^{n}\), we get to use \(500e^{0.10\cdot n}\).

Answer 22

ahhh kk

Answer 23

500e^0.10-10?

Answer 24

Divided by....

Answer 25

wait it is not pe^r%T

Answer 26

pe^r/100time t

Answer 27

\(500\cdot\dfrac{e^{0.10\cdot n} - 1}{e^{0.10} - 1}\)

You must add up 10 of them.

Answer 28

it same way we didnt learn that that why i dont know that kk

Answer 29

2113 the answer

Answer 30

It will be of great value to you to learn to add up a geometric series.

500 + 500*r + 500*r^2 + ... + 500*r^9

You will NEVER struggle with finding the "right" formula, again, if you concentrate on this fundamental principle.

Answer 31

No, no. Again, $500*10 = $5,000! It MUST be greater than that? Never be satisfied with a value less than $5,000.

Answer 32

i found sorry 8591

Answer 33

Where did "-10" come from?

\(e^{0.01\cdot 10} = e^{0.10} = 1.1051709180756476152426726271225\)

Answer 34

8591 is no good. Something went wrong. Give it another go.

Answer 35

kk

Answer 36

first stepe 11/100 =0.11 so e^0.11*10 -1=2.00

Answer 37

I wondered if you had done that. Read Part B of the problem statement, again.

Answer 38

kk

Answer 39

10% so 10/100=0.1 so e^0.1*10-1=

Answer 40

i am doing same annually but continuously

Answer 41

so e^0.1*10-1=1.718

Answer 42

(1.718/0.10)*500

Answer 43

I would certainly recommend using more decimal places.

Answer 44

mmm

Answer 45

The Numerator

\(\dfrac{1.718}{1.718281828459} = 0.9998359\) and is only a small error, 0.02%.

\(\dfrac{0.10}{0.105170918} = 0.950833\) and is a whopping 5% error!

Are you sure you're okay with a deliberate error that size?

Answer 46

can you explain me how

Answer 47

1.718.1718.92 ?

Answer 48

How did you get 1.718?

The value of e-1 is 1.718281828459045... You must DECIDE what level of precision is sufficient for your needs. Generally, if you are dealing in thousands of dollars, you will need 5 ir 6 decimal places to have any reliablility at all in the pennies. You MUST look at the first decimal place you lop off and decide how important it is and what difference it will make.

Let's look at the denominator.

You used 0.10 ==> 1/0.10 = 10
One more decimal place 0.105 ==> 1/0.105 = 9.524
That's quite a difference!
One more decimal place 0.1051 ==> 1/0.1051 = 9.5147
One more decimal place 0.10517 ==> 1/0.10517 = 9.50842

You can't just go about it willy nilly. You must make choices.

Answer 49

denomerator it is e^0.10-1

Answer 50

=0.1051809181