Question

You estimate that you will need $11620 at the end of year 7. How much do you have to set aside today if your bank pays 18.26% per year compounded quarterly?

Answer 1

@zepdrix

Answer 2

oh hey

Answer 3

I have a solution...

Answer 4

FV = PV (1+IR/n)^n Is this the equation? I did it from memory, If so solve for PV

Answer 5

we have ia = (1+ (r/m))^m-1

Answer 6

That is the effective annual interest rate.

Answer 7

I have an answer, but I am not sure about it. I got $8501.62.

Answer 8

r = nominal interest rate per year
m = number of compounding subperiods per year
r/m = interest rate per interest period
mn = number of compounding subperiods in n years

Answer 9

this monthly, quartly stuff is confusing me

Answer 10

I having difficulty understanding r, ia, and m

Answer 11

Why m-1? Let me re-read the question.

Answer 12

Sorry os locked up

Answer 13

we need to solve for p so this is what I did...

ia = (1 + (0.06/30)^30-1 = 6.17%

then I used P = F(P/F,6.17%,30) = 39,719

Answer 14

what is nominal interest rate and effective interest rate?

Answer 15

Yes I don't know what ia could be..
r is the 18.26 / 4
M would be 7 * 4 28

Answer 16

My memory equation was wrong. i got my book out.

Answer 17

i - r/m which is the interest rate per interest period i though and r = mn which is the number of compounding subperiods in n years

Answer 18

suupose to be = not -

Answer 19

since we have 18.26% quartly do I need to figure out the interest rate per year?

Answer 20

Compound Amount Factor (Single Payment)

F = P (1+i)^N Future F Present P i ?? N number of periods

Answer 21

1/4(12) = 3 so there are 3 months in one subperiod? 3+3+3+3 = 12 each 3 represents a quarter

Answer 22

That is how I am interrupting this

Answer 23

bank pays 18.26% per year, compounded quarterly so each quarter they pay 18.26/4

Answer 24

so r = 18.26%?

Answer 25

P = 11620 / (1+18.26/4)^(4*7)

Answer 26

i = r/m = 4.56% so this is per subperiod? so every 3 months we have an interest of 4.56%

Answer 27

Yes in your equation r is 18.26%

Answer 28

I just answer the question above myself.. lol

Answer 29

A mistake .....

P = 11620 / (1+0.182626/4)^(4*7) r must be in decimal format

Answer 30

Another mistake ....


P = 11620 / (1+0.1826/4)^(4*7) r must be in decimal format

Answer 31

yeah I just noticed that now... I was doing the calculation over again

Answer 32

I got an answer of P = 8501.62

Answer 33

That's what i got from my program

from my equation Now i get $3329.57

Answer 34

I must have did the equation wrong.

Answer 35

the equataion is P = F(1+i)^-n

Answer 36

I want to go back and do some previous problems. I really want to understand these problems. here is question 5

Stan and Star are buying a house for $239856. The bank is offering a nominal annual mortgage rate of 6% for 30 years, compounded monthly. What will their monthly loan payment be?

Answer 37

P= ?
F = 239856
n = 30

Answer 38

I was using N as 7*4. It should be just 7, I guess.

Answer 39

Go to the next question...

No P is the cost of the house today

P= 239856
n = 30
F = is a don't care I need a house now
r = 0.06

A = the amount paid each month, the monthly loan payment

Answer 40

let me solve this. I did this wrong because I inturrpted it wrong

Answer 41

how do I solve this one? I need i...

Answer 42

6% over 30 years would be 0.002 = 0.02% every year?

Answer 43

After working this problem I think the last problem N is equal to 7*4 = 28

I have bought and paid for a house. I know my answer for this one is correct.

I am going back to work on the first problem. To prove that N is 28, maybe.

Answer 44

No, but I wish 6% per year 0.06/12 per month

Answer 45

Oh i see 6% per year why not 6%/12 = 0.50 which is 50% why is it 0.06/12 = 0.005 how do you know if r = to a percentage or decimal? I am confused.

Answer 46

I these equations always use decimals for interest.

Answer 47

so it's 0.005 = 0.05% per year over 30 years? Am I interrupting that correctly?

Answer 48

so when dealing with these problems I need n because n is in therms of years.

so r interest rate that is not compounded and i is interest rate that is compounded?

Answer 49

The answer to the first question is $3329.57 use N = 28 in your calculation

Here is the excel proof amount compounded per quarter for 7 years

11620 0.1826/4
0.04565

0 $3,329.57 $151.99
1 $3,481.56 $158.93
2 $3,640.50 $166.19
3 $3,806.69 $173.78
4 $3,980.46 $181.71
5 $4,162.17 $190.00
6 $4,352.17 $198.68
7 $4,550.85 $207.75
8 $4,758.60 $217.23
9 $4,975.83 $227.15
10 $5,202.97 $237.52
11 $5,440.49 $248.36
12 $5,688.85 $259.70
13 $5,948.54 $271.55
14 $6,220.09 $283.95
15 $6,504.04 $296.91
16 $6,800.95 $310.46
17 $7,111.41 $324.64
18 $7,436.05 $339.46
19 $7,775.51 $354.95
20 $8,130.46 $371.16
21 $8,501.61 $388.10
22 $8,889.71 $405.82
23 $9,295.53 $424.34
24 $9,719.87 $443.71
25 $10,163.58 $463.97
26 $10,627.55 $485.15
27 $11,112.69 $507.29
28 $11,619.99

Answer 50

7*4 = 28 why is it 28?

Answer 51

Sorry I was off on a tangent..

so when dealing with these problems I need n because n is in terms of years. NO
N is in terms of periods
if compounded monthly a period is a MONTH or 12 for a year
if compounded quarterly a period is 3 months or 4 per year

so r interest rate that is not compounded and i is interest rate that is compounded?
r is the annual rate i is the rate for the period


Digest this for a while. You were even confusing me for a second earlier.

Answer 52

7*4 = 28 why is it 28?

7*4 = 28 why is it 28? 7 years and 4 times a year 7*4 = 28

The first problem was compounded quarterly for 7 years....

You estimate that you will need $11620 at the end of year 7. How much do you have to set aside today if your bank pays 18.26% per year compounded quarterly?

Answer 53

okay so a period in this problem is 3 months so there are 4 periods and we have 7 years so 7*4 = 28.

Thank you for explaining to me what a "period" can be in terms of. That make a lot of confusion go away.

Answer 54

Great now in the current problem....

30 years monthly payments How many periods N ?

Answer 55

360 because every period is 1 month so we have 30*12 = 360 months

Answer 56

Yes!

Answer 57

I am probably going to write your last statement down in my textbook somewhere so I can reference if I get confused. That helped out a lot though.

Answer 58

Stan and Star are buying a house for $239856. The bank is offering a nominal annual mortgage rate of 6% for 30 years, compounded monthly. What will their monthly loan payment be?
I am going to try go to figure this out.

Answer 59

I did it on the calculator, but I trying to find the right equation.

Answer 60

SO in this case the r = 6% because it's an annual interest rate?

Answer 61

that is r 6%

use i as 0.06 / 12 = 0.005

Answer 62

kk that makes a lot of sense

Answer 63

I am working on the problem

Answer 64

A = 1438.05

Answer 65

YES! I got that answer.....


Use a Series Present-Worth Factor (uniform Series)

A = [ i (1+i)^N ] / [ ((1+i)^N) - 1] the - 1 is NOT part of the exponent

Answer 66

yeah I used A = P[i(1+i)^n/(1+i)^n-1]

Answer 67

And it makes logical sense. When I first did it I used N = 30 and got a very large monthly payment.

Answer 68

yeah if you use 30 you get A = 8629.75

Answer 69

That would be most folks, entire both paychecks for a couple.

Answer 70

Cushing, Inc. invested $226821 in an account paying 7% per year, compounded monthly. How much will Cushing have in its account in 9 years?

Answer 71

F = 425102.69

Answer 72

@retirEEd

Answer 73

For retirement planning, you decide to deposit $724 at the end of every quarter and increase your deposit by $38 each quarter . How much will you have at the end of 25 years if the bank pays a nominal annual rate of 2% compounded quarterly?

Answer 74

F = 425102.69
yes

Answer 75

^^^working on this one now. so i've concluded that n = 100 quarters because we have 1 perirod =

Answer 76

For retirement planning, you decide to deposit $724 at the end of every quarter and increase your deposit by $38 each quarter . How much will you have at the end of 25 years if the bank pays a nominal annual rate of 2% compounded quarterly?

Answer 77

here I got n = 25yr*4 = 100 quarters.

A = 725 and G = 38 because it's increases every quarter. I was thinking this is an arithmetic gradient series, but I don't have an euqtion for finding F knowing G, F/G.

Answer 78

What is the starting point? What is the ending point? There might be 99 periods since the first deposit is at the END of the first quarter.

Answer 79

hold on i think i figured it out

Answer 80

Say you start working on Jan 1, 2000. You make your first payment on March 31, 2000

You retire 25 years later on Dec 31, 2025 and you make your last payment.

I get 3 payment in the first year and 4 * 24 until Dec 31, 2025 N = 99

Answer 81

I don't know how to do these gradient ones on my calculator so I have use my book's equation.

Answer 82

you can't do these on the calculator. you have to do them by hand. I almost got the answer.

Answer 83

I got F = 316,573.70

Answer 84

Still working ....

Answer 85

I didn't get that. My number is smaller. What i did you use?

Answer 86

I used P=A(P/A,i,n) + G(+/G,i,n) got P then solved for F

F = P(1+I)^n

Answer 87

G(P/G,i,n)*

Answer 88

I see one of my mistakes hold on ...

Answer 89

Okay I got $316,764.99 which is pretty close.

There might be some round off errors in excel

Answer 90

or excel is more accurate

Answer 91

Well I am out of here. I have class in an hour and I need to eat something. Thanks for your help today! take care.

Answer 92

I always forget to add the gradient in this case $38 to the previous value plus the gradient.

I was just using 725 + 38 for the entire 25 years past the first quarter.

Answer 93

Bye

Answer 94

Oh I see

Answer 95

later