Answer :
Answer :
Depends on the rate compound interest is accrued. See answers.
Step-by-step explanation:
We need the compound interest formula which is:
[tex]A = P (1+\frac{r}{n} )^{nt}[/tex]
A = final amount
P = initial principal balance
r = interest rate
n = number of times interest applied per time period
t = number of time periods elapsed
It doesn't say how frequently the interest is compounded, so we will do monthly, quarterly, and yearly.
MONTHLY
So we know the car costs $25,480 and he made a down payment of $10,000. By subtracting the down payment from the purchase price we find the loan amount.
$25,480 - $10,000 = $15,480
P = 15,480
r = 4.75% = .0475
n = 12 (12 months in a year)
t = 2
Plug everything into the compound interest formula.
[tex]A = P (1+\frac{r}{n} )^{nt}[/tex]
[tex]A = 15480(1+\frac{.0475}{12})^{12*2}[/tex]
[tex]A = 15480(1+\frac{.0475}{12})^{24}[/tex]
[tex]A = 15480(1+.00396)^{24}[/tex]
[tex]A = 15480(1.00396)^{24}[/tex]
[tex]A = 15480*1.0992[/tex]
[tex]A = $17016.14[/tex]
Mr. Lee paid $17,016.14 when the bill came due at 2 years with interest compounded monthly.
QUARTERLY
P = 15,480
r = 4.75% = .0475
n = 4 (4 quarters in a year)
t = 2
[tex]A = P (1+\frac{r}{n} )^{nt}[/tex]
[tex]A = 15480(1+\frac{.0475}{4})^{4*2}[/tex]
[tex]A = 15480(1+\frac{.0475}{4})^{8}[/tex]
[tex]A = 15480(1+.0119})^{8}[/tex]
[tex]A = 15480(1.0119)^{8}[/tex]
[tex]A = 15480*1.099[/tex]
[tex]A = 15480(1.099)[/tex]
[tex]A = 17013.20[/tex]
Mr. Lee paid $17,013.20 when the bill came due at 2 years with interest compounded quarterly.
YEARLY
P = 15,480
r = 4.75% = .0475
n = 1
t = 2
[tex]A = P (1+\frac{r}{n} )^{nt}[/tex]
[tex]A = 15480(1+\frac{.0475}{1})^{1*2}[/tex]
[tex]A = 15480(1+\frac{.0475}{12})^{2}[/tex]
[tex]A = 15480(1+.0475})^{2}[/tex]
[tex]A = 15480(1.0475)^{2}[/tex]
[tex]A = 15480*1.0973[/tex]
[tex]A = 16985.53[/tex]
Mr. Lee paid $16,985.53 when the bill came due at 2 years with interest compounded yearly.