Question

Find the monthly payment for the loan.
New car financing of 3.3% on a 30-month $12,850 loan.

I know to use the amortization formula, but the 30-months totally threw me off and I'm not sure what number to use for 'n' and 't'. Please help!

Answer 1

what is the amortization formula your book gives you?

Answer 2

\[m=\frac{ P(\frac{ r }{ n }) }{ 1-(1+\frac{ r }{ n })^{-nt} }\]

Answer 3

@jim_thompson5910

Answer 4

ok one sec

Answer 5

ok t is time in years

30 months = 30/12 = 5/2 = 2.5 years

so t = 2.5

-----------------------------------

n is the payment frequency. In this case, it happens monthly which means n = 12

r = 3.3/100 = 0.033 since 3.3% = 0.033

Answer 6

Thank you so much for clearing that up for me!!! It makes so much more sense now!

Answer 7

I'm glad it's clicking now

Answer 8

@jim_thompson5910 Thank you! I got the correct answer! Do you mind helping me with another problem?
How much interest (to the nearest dollar) would be saved on the following loan if the home were financed for 15 rather than 30 years?
A $128,000 home bought with a 20% down payment and the balance financed for 30 years at 8.5%

Answer 9

how much is paid for the down payment?

Answer 10

I'm not sure that was all the information I was given

Answer 11

well it says "20% down payment" on the $128,000 home

Answer 12

I don't know how to figure that out

Answer 13

you take 20% of the home's value

Answer 14

$6400?

Answer 15

or $25600?

Answer 16

it should be 0.20*128,000 = 25,600

Answer 17

you have to pay $25,600 up front before you can even think about getting the mortgage

Answer 18

the remaining about you didn't pay, 128,000 - 25,600 = 102,400

is the amount you are financed. Ie, it is the amount that is lent to you.

Answer 19

amount*

Answer 20

so P = 102400

Answer 21

8.5% = 0.085

so r = 0.085

Answer 22

n = 12 because mortgages are paid monthly

t = 30 (at first)

Answer 23

is $787.37 the correct answer? And then I would do the same with t=15

Answer 24

that is the monthly payment for the 30 yr mortgage

Answer 25

how much total will you pay back over the entire 30 yr period?

Answer 26

is that done with an annuity formula?

Answer 27

nope, multiply the monthly payment by 360

why 360? because there are 360 months in 30 years

30 years = 30*12 = 360 months

Answer 28

simple example: let's say you pay $100 a month for 30 months, you would pay back a total of 100*30 = 3,000 dollars

Answer 29

$283,452.27

Answer 30

I'm getting $283,453.20

Answer 31

I redid it and got the same answer as you

Answer 32

now we subtract the initial amount borrowed ($102,400) from the total ($283,453.20)

Answer 33

so...

283,453.20 - 102,400 = 181,053.2

Answer 34

this means that the total amount of interest and interest only is $181,053.20

Answer 35

again this is all for the 30 yr mortgage

Answer 36

Okay so that completes the 30 yr part? Do I do the same for the 15 yr?

Answer 37

yes, follow the same steps for the 15 yr one

Answer 38

then subtract the two interest only figures to get the amount you save

Answer 39

And that will be the answer?

Answer 40

correct. After you round to the nearest dollar

Answer 41

$101946.60

Answer 42

I'm getting the same answer. Nice work.

Answer 43

Thank you so much for your help!! I really appreciate it!

Answer 44

you're welcome

Answer 45

@jim_thompson5910 I really hate to be a bother, but if you don't mind could you help me with two more problems? I tired to do both of them, but I just can't seem to figure them out!

1. Melissa agrees to contribute $500 to the alumni fund at the end of each year for the next 5 years. Shannon wants to match Melissa's gift, but he wants to make a lump-sum contribution. If the current interest rate is 7.5% compounded annually, how much should Shannon contribute to equal Melissa's gift? (Round your answer to the nearest cent.)

2. A $1,000,000 lottery prize pays $50,000 per year for the next 20 years. If the current rate of return is 8.25%, what is the present value of this prize? (Assume the lottery pays out as an ordinary annuity. Round your answer to the nearest cent.)

Answer 46

ok let me think them over for a moment

Answer 47

I think for the first one, you use the future value of annuity formula. Do you have that formula with you?

Answer 48

Yeah I do

Answer 49

what formula do they give you?

Answer 50

\[P= m(\frac{ 1-(1+\frac{ r }{ n }^{-nt}) }{\frac{ r }{ n } })\]

Answer 51

m = 500 is the amount Melissa pays per year

r = 0.075 (since 7.5% = 7.5/100 = 0.075)

n = 1 (compounded annually)

t = 5 (for five years)

plug those values into the formula to get ???

Answer 52

$2022.94

Answer 53

I got that as well

Answer 54

It showed up correct on my homework! :D

Answer 55

that's the amount Shannon needs to contribute

Answer 56

As for the next one, you'll most likely use the present value formula. What formula do they give you?

Answer 57

The same one as before?

Answer 58

Nevermind I found it, just a second

Answer 59

no I don't think you'll use the future value formula

Answer 60

\[P=A(1+\frac{ r }{ n })^{-nt}\]

Answer 61

hmm does it give you a present value of annuity formula?

Answer 62

The present value of annuity formula that I was given is the one I used from before

Answer 63

so this?

\[P= m(\frac{ 1-(1+\frac{ r }{ n }^{-nt}) }{\frac{ r }{ n } })\]

Answer 64

yeah

Answer 65

it seems odd how you'd use that formula though

Answer 66

It's okay if you can't figure out how to solve it!

Answer 67

Would it be the ordinary annuity formula?

Answer 68

I did find this page

http://www.financeformulas.net/Present_Value_of_Annuity.html

Answer 69

I wonder if you are given a similar formula?

Answer 70

I don't have a formula like that, but maybe it will work

Answer 71

using that formula, the inputted values are

P = 50,000
r = 0.0825
t = 20

Answer 72

would n be 12?

Answer 73

well I'm using the formula given on this page

http://www.financeformulas.net/Present_Value_of_Annuity.html

oh I completely glossed over n for some reason. The variable n represents the number of periods. In this case, there are 20 periods (20 years). One period is one payment. So in a way, this page is treating "t" like "n". A bit confusing if you ask me.

Answer 74

n = 20 in this case because 20 payments are made

Answer 75

each payment is coming from the lottery commission and it goes to the lottery winner

Answer 76

$481907.39

Answer 77

got the same

Answer 78

Yay!!! THANK YOU SOOOOOOO MUCH!! I cannot thank you enough, I would have no idea what to do without you!

Answer 79

I'm glad I could help out and that it is making sense now.