Question

Fred purchased a boat for $8,645. He made a down payment of $775. He applied for a six-year installment loan with an interest rate of 11.4% in the amount of $7,870. What is the total cost of the boat after six years?

$11,677.24

$8,767.18

$9,630.53

$10,902.24


No idea how to do this please help!

Answer 1

So you're assuming that you are making equal-sized payments every year for 6 years?

Answer 2

@Compassionate

Answer 3

And that's the annual interest rate?

Answer 4

Im not sure? Im really confused

Answer 5

Is this taken from a textbook? If so, what's the name of the chapter?

Answer 6

I have this formula but not sure how to use it

Answer 7

Its called "purchasing costs"

Answer 8

Is this for a math class?

Answer 9

Yes

Answer 10

Do they mention anything about "annuities"?

Answer 11

No they haven't

Answer 12

Have they mentioned any of the terms (from this question) in any previous questions?

Answer 13

Yes they have I can show you an example question

Answer 14

Ok, great--that helps a lot. Now give me a minute...

Answer 15

Okay! thank you for your help I really appreciate it!

Answer 16

Yeah--that problem was giving me problems (I got an answer that wasn't a possible choice). But that picture clarified some things...

Answer 17

First, they are assuming that you are making monthly payments at an annual rate of 11.4%

(I was assuming they were annual payments)

Answer 18

That formula is the "annuity" thing I was talking about...

Answer 19

Okay so where do I go from there?

Answer 20

I'll explain the letters in the formula as they relate to your question.

Answer 21

First, the "P" (which stands for "principal") is the amount you're borrowing (i.e $7870)

Answer 22

Ok thank you

Answer 23

the "t" is the number of years (in this case 6) and "n" is the number of payments made per year (these are monthly payments, so "12").

Answer 24

Whats "i" then?

Answer 25

Lastly, the "i" is the interest rate. BUT WAIT! It's NOT equal to 11.4% because that is the ANNUAL interest rate. And, the convention with credit cards, etc. is to get that number by multiplying the per-period interest rate by the number of periods in the year to get that annual rate.

Anyway, my point is that "i" is equal to:
\[\frac{ 0.114 }{ 12 }= \]

=0.95

Answer 26

Ohh Okay! I understand!

Answer 27

Anyway, to solve:

1.) plug in those numbers to get "M", the monthly payment
2.) multiply M by "72" (the number of monthly payments you have to make)
3.) Add back the $775 down payment to get the total cost of the boat

Answer 28

Now, solve this and tell me what you get...

Answer 29

Okay will do give me one second

Answer 30

Im not getting the right answer at all im doing something wrong

Answer 31

what are you getting?

Answer 32

for instance, what did you get for "M"

Answer 33

I got 393.5

Answer 34

ok, what did you get for your numerator in that formula?

Answer 35

and what did you get in the denominator?

Answer 36

I'm gonna try to reverse engineer your answer...

Answer 37

This is what I typed in the calculator

Answer 38

First, your monthly interest rate is 0.95%, so it should go in as

i = 0.0095

Answer 39

that big number on the bottom was (1=.95)^72

Answer 40

ohh i didnt know that

Answer 41

Yeah, it should be:

(1.0095)^72

Answer 42

Okay Ill try it again

Answer 43

Yeah, that would be like getting a 95% interest rate per year for 72 years!

Answer 44

7795.235
?

Answer 45

Is that what you got in the numerator?

Answer 46

Ohh wow! I didnt think of that!

Answer 47

No thats M

Answer 48

just tell me the numerator

Answer 49

0.01876631

Answer 50

then multiply that by P

Answer 51

147.69

Answer 52

and what was your denominator?

Answer 53

.975401031

Answer 54

so just divide the two

Answer 55

147.69 / 0.975401031 = ?

Answer 56

151.41

Answer 57

11,676.85?

Answer 58

Not quite... More like $151.42. :)

Answer 59

Like is 11,677 the answer?

Answer 60

I don't see why not...

Answer 61

THANK YOU SO MUCH FOR ALL YOUR HELP!

Answer 62

Does it all make sense now?

Answer 63

Yes it does! Thank you!

Answer 64

Ok, great! Good luck with the rest of your work.

Answer 65

Thank you!

Answer 66

Any time!