Question

Using the compound interest formula, determine the total amount paid back and the monthly payment. Buying a $6000 used sedan taken out with $500 paid up front and the rest borrowed at 8.3%annual interest compounded daily (365 days per year) over 2 years.

Answer 1

The final value of an investment or loan with compound interest is given by:

`FV=P(1+(r)/(m))^(m\cdot t)`

Where P is the initial value (principal or loan), r is the annual interest rate, t is the duration of the investment/loan, and m is the number of compounding periods per year.

The following values are given in the problem:

P = $6000 - $500 = $5500

r = 8.3% = 0.083

t = 2 years

m = 365

Applying the formula:

`FV=5500(1+(0.083)/(365))^(365\cdot2)`

Calculating:

`FV=5500(1+0.0002273926)^(730)`

FV = $6493.03

The total amount paid back is $6493.03

This is equivalent to an approximate monthly payment of:

`R=($ 6493.03 $)/(24)=270.54`

The monthly payment is approximately $270.54