Question

You purchase a new car for $24,000. If you obtain a 5 year bank loan at 2.75% compounded monthly, what is your monthly loan payment?

Answer 1

The monthly loan payment is of $458.88.

Explanation:

Compound interest:

The compound interest formula is given by:

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

Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the time in years for which the money is invested or borrowed.

Amount owed after 5 years:

Loan of 24000 means that
`P = 24000`

5 years means that
`t = 5`

Interest rate of 2.75% means that
`r = 0.0275`

Compounded monthly means that
`n = 12`

The amount is A(5). So

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

`A(5) = 24000(1 + (0.0275)/(12))^(12*5)`

`A(5) = 27533`

What is your monthly loan payment?

$27,533 in 5 years = 5*12 = 60 months. So

27533/60 = 458.88

The monthly loan payment is of $458.88.