Question

Eaton purchased a boat for $11,975. He made a down payment of $3,500. He applied for a five-year installment loan with an interest rate of 11.2%. What is the total cost of the boat after five years?

$13,316.20

$14,606.60

$15,693.69

$11,106.81

Answer 1

http://ncalculators.com/loan/installment-loan-payoff-calculator.htm

Answer 2

principal amount would be 11975 - 3500

Answer 3

\[B_n=B_ok^{c}-P\frac{1-k^c}{1-k}\]
assuming we want a zero baolance after 5 years; and i assume monthly payments
\[0=B_ok^{12*5}-P\frac{1-k^{12*5}}{1-k}~:~k=1+\frac r{12}\]
\[B_ok^{12*5}=P\frac{1-k^{12*5}}{1-k}\]
\[B_ok^{12*5}\frac{1-k}{1-k^{12*5}}=P\]
5 years worth of payments, minus the intial amount; gives us total cost loan

Answer 4

well, i spose if we just add up the payments itll be fine ... i was thinking total interest cost on the loan

Answer 5

I'm not familiar with that equation, what does everything stand for?

Answer 6

did you try the website

Answer 7

Bo is initial balance (loan amount)

k is a clean up variable to represent that compounding stuff

and P is the Payments

Answer 8

I don't really like using website calculators, they're often wrong or make an error @ivettef365

Answer 9

assuming monthly payments of 185.12 ... and there are 60 of them in 5 years

Answer 10

Can you plug everything in for me? I'm still confused

Answer 11

what is your inital loan amount?

Answer 12

8475?

Answer 13

good, and what is your compounding setup?

1 + r/12

Answer 14

1 + 0.112/ 12

Answer 15

good, and putting it all together we get

P = 8475k^(12*5)(1-k)/(1-k^(12*5))

since there are 12*5 payments .. 60 payments

60(8475k^(12*5))(1-k)/(1-k^(12*5)), k=1+.112/12

http://www.wolframalpha.com/input/?i=60%288475k%5E%2812*5%29%29%281-k%29%2F%281-k%5E%2812*5%29%29%2C+k%3D1%2B.112%2F12

Answer 16

Aaaahhh I'm still confused

Answer 17

Idk how to plug this into my calculator

Answer 18

60 * 8475 * (1+.112/12)^(60) * (1-(1+.112/12)) / (1-(1+.112/12)^(60))

Answer 19

might help to approximate that k stuff

Answer 20

yeah formula for solving for monthly payments is a bit complex...what class is this for?
you would be best to use a financial calculator

total payments = 60*monthly payment

Answer 21

you could off have the answer using website, I got the right answer

Answer 22

yeah but cant use website on test or in class....get a financial calculator like a TI BAII

Answer 23

I have a TI-36X Pro

Answer 24

@amistre64 I plugged everything into my calculator and got 11,106.81

Answer 25

@murrcat , that is correct

Answer 26

Sweet

Answer 27

i developed my own formula .... which is a less "simplified" version of most texts i think

Answer 28

11,106.81 was wrong :c

Answer 29

you know what, we forgot to add in the downpayment as part of the cost ....

Answer 30

11,100
3,500
-------
14,600