Question

Fiona installed a new pool for $9,940 using a 12-month deferred payment plan with an interest rate of 22.53%. What is the balance after the deferment period if payments of $397 are made each month?

Answer 1

Anyone want to help me out?

Answer 2

this is the third of these, i am wondering if you are given a formula to use
it would make it a lot easier

Answer 3

lol hey whats up satellite73 =D

Answer 4

a=p(1+1/n)^nt...............?

Answer 5

Hint: Use the formula

A = P(1 + r/n)^(nt)

If the interest is compounded monthly (most likely the case), then n = 12

Answer 6

yeah but that doesn't really do it

Answer 7

that tells you what you would get after \(t\) years if you invest \(P\) at a rate of \(r\) compounded \(n\) times per year

Answer 8

which is how credit card balances are computed (if compound interest is used)

Answer 9

this is a different question
how much is left on the loan

Answer 10

$7,761.84

$9,940.00

$5,176.00

$12,425.84

Answer 11

keep in mind no payments are made during the deferred payment period

Answer 12

but the interest changes, because the principle changes every month

Answer 13

which is why compound (instead of simple) interest is used

Answer 14

i know this are the choices but these problems make no sense to me

Answer 15

these*

Answer 16

maybe i am confused, but i understand it to mean this:
if you pay $397 each month, how much is left on the loan
if you are charged no interest, then it is easy
if you are charged 22.53% divided by 12 each month, then the principle of the loan changes

Answer 17

no payments are made during the deferred payment period

Answer 18

it is not the same as saying "how much would 9,940 be worth at 22.53% in one year?"

Answer 19

sure you can make payments, but you are allowed to not make them

We're assuming no payments are made, which is why the balance goes up

Answer 20

basically this is saying that you bought an item for some specified amount of money, then you wait 12 months or 1 year til you make payments

during that period, the balance goes up because interest is added

Answer 21

@jim_thompson5910 you may certainly be right, but then why day

What is the balance after the deferment period if payments of $397 are made each month?

Answer 22

*say

Answer 23

because problems love to throw extra/useless info a lot of the time

Answer 24

i take this to mean that you pay $397 each month for the first year

Answer 25

and keep in mind that some other problems like to ask follow up questions

ex: when will the balance be fully paid off?

Answer 26

so how would i set this up then?

Answer 27

you can, but you don't have to...because the payments are deferred

Answer 28

again you may be right, but i am sceptical
in real life if you have deferred payment you can start buying down the principle right away

Answer 29

yes, you *can*, but again don't have to

you can't get away with not paying down credit debt if it wasn't deferred because you would eventually be legally responsible for doing so (or you would have your credit ruined)

with deferred plans, you can wait til the deferred payment period is over when you start making your first payments

Answer 30

but you're 100% correct, it's smart to pay down your debt asap

this is esp true at such a high interest rate

Answer 31

to start Osniel, use the formula

A = P(1 + r/n)^(n*t)

where

P = principal (amount invested...which in this case is the original balance)
r = interest rate
n = compounding frequency
t = time in years

Answer 32

i am still confused
why the word "if"
What is the balance after the deferment period IF payments of $397 are made each month

Answer 33

but saying "deferment period" implies that payments were deferred

Answer 34

is it really a red herring?

Answer 35

why mention there is a deferred period? why not leave that part out

Answer 36

i thought it meant you made those payment, in which case it would be a totally different formula, but i will believe you

Answer 37

A=9,940+(0.2253/12)^12*0.2253? is this right

Answer 38

yes if you made the payments, then that formula wouldn't apply

Answer 39

more like

A = 9940(1 + 0.2253/12)^(12*1)

Answer 40

oh so is it 12425

Answer 41

12,425.84 yes

Answer 42

thank you both of you you two are great teachers

Answer 43

thanks jim

Answer 44

np