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Dallas Wright took out a 48-month fixed installment loan of $6500 to purchase a new all-terrain vehicle (ATV). He began making monthly payments of $227.50. Instead of making his 25th payment, Dallas decides to repay his loan in full. How much interest will Dallas save?

Respuesta :

so as a matter of an ordinary annuity, 6,500 was loaned at some rate "r", whatever that is, the payment or deposits to be made are calculated, and end up at 227.50 monthly, for 48months

so Dallas is going to be paying 227.50 * 48 total, that includes the 6,500 plus interest

now, he makes 24 payments, that is, pays for 2 years, 12 months and 12 months

then he decides that, instead of making the 25th payment, to begin the 3rd year, he says, whatever, I'll just pay the full amount, whatever the remainder is

so 24months is half of 48months

each payment pays part of the interest and part of the principal
without calculating the rate, which we could

I'd say at the 24month, he's already paid half the interest and half the principal 

227.50 * 48 = 10,920
half that is  5,460, that's how much he's paid by the 24th payment, which should include half of the principal 6,500 or 3,250

so... for his 25th payment, he decides no to pay the rest 227.50 * 24, or 5,460, but just the half of the principal, skipping the interest, or just 3,250

so.. he'd end up saving 5,460( what he would have paid with interest) minus 3,250( half of the principal remaining)

Dallas Wright will save [tex]\$\ 2210[/tex] interest.

What is interest ?

Interest is the amount which is charged on lent or borrowed money at specific rate.

i.e. Final Amount [tex]-[/tex] Principal [tex]=[/tex] Interest

We have,

Total value of loan [tex]=\$\ 6500[/tex]

Total time of loan [tex]=48[/tex] months [tex]=4[/tex] years

Monthly installment [tex]=\$ \ 227.5[/tex]

Till now [tex]24[/tex] installments paid.

So,

Total amount to be paid in [tex]48[/tex] installments [tex]=48\ *\ 227.5=\$\ 10,920[/tex]

Now,

Total interest to be paid [tex]=\ 10920-6500=\$\ 4420[/tex]

This means that rate of interest will be,

As no mention of type of interest, we will use Simple Interest formula,

Simple Interest [tex]=\frac{Principal\ *\ Rate\ *\ Time}{100}[/tex]

i.e.

[tex]4420=\frac{6500\ *\ Rate\ *\ 48}{100\ *\ 12}[/tex]

⇒ [tex]R= \frac{4420}{65\ *\ 4}[/tex]

[tex]R=17\%[/tex]

i.e. Rate of interest [tex]R=17\%[/tex]

Now,

So,

Total amount paid in [tex]24[/tex] installments [tex]=24\ *\ 227.5=\$\ 5460[/tex]

Interest paid till [tex]24[/tex] months [tex]=\frac{6500*24*17}{100*12}=\$\ 2210[/tex]

So,

Money paid as a principal till [tex]24[/tex] months [tex]=5460-2210=\$\ 3250[/tex]

So, Amount left to pay [tex]6500-3250=\$\ 3250[/tex]

So, Dallas would save as interest [tex]=10920-5460-3250=\$\ 2210[/tex]

Hence, we can say that Dallas Wright will save [tex]\$\ 2210[/tex] interest.

To know more about interest click here

https://brainly.com/question/11339060

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