Question

A certain college graduate borrows $8000 to buy a car. The lender charges interest at an annual rate of 10%. Assuming that interest is compounded continuously and that the borrower makes payments continuously at a constant annual rate k, determine the payment rate k that is required to pay off the loan in 3 years. Also determine how much interest is paid during the 3-year period.

Answer 1

Answer:

The payment is $k=\ 3216.92$.

Interest paid during the 3-year period is $I_{T}=\ 1651.76$

Step-by-step explanation:

Hi

The Payment amount

We are going to use the formula below with $VP=\ 8000, i=10\%$ and $n=3$.

$k=\frac{VP}{[\frac{1-(1+i)^{-n}}{i}] } =\frac{8000}{[\frac{1-(1+0.1)^{-3}}{0.1}] }=3216.92$

Interest paid during the 3 year

• First period

$I_{1}=VP*i=8000*0.1=800$

$CS_{1}=k-I_{1}=3216.92-800=2416.92$

$Balance_{1}=VP-CS_{1}=8000-2416.92=5583.08$

• Second period

$I_{2}=B_{1}*i=5583.08*0.1=558.31$

$CS_{2}=k-I_{2}=3216.92-558.31=2648.61$

$Balance_{2}=VP-CS_{2}=5583.08-2648.61=2924.47$

• Third period

$I_{3}=B_{2}*i=2924.47*0.1=292.45$

• Sum of Interest paid during the 3 years

$I_{t}=I_{1}+I_{2}+I_{3}=800+558.31+292.45=1651.76$