Question

Quantitative Problem: You need $20,000 to purchase a used car. Your wealthy uncle is willing to lend you the money as an amortized loan. He would like you to make annual payments for 4 years, with the first payment to be made one year from today. He requires a 8% annual return. What will be your annual loan payments? Round your answer to the nearest cent. Do not round intermediate calculations. $ 6038.4 How much of your first payment will be applied to interest and to principal repayment? Round your answer to the nearest cent. Do not round intermediate calculations. Interest: $ Principal repayment

Answer 1

Answer:

Ans. the annual payment will be $6,038.42, applied to interest $1,600, applied to principal $4,438.42

Explanation:

Hi, in order to find the amount to be paid for 4 years, we need to use the following formula.

$PresentValue=\frac{A((1+r)^{n}-1) }{r(1+r)^{n} }$

Where:

r= interest rate

n= periods of periodic payment

A= periodic payments

Present Value= amount of money of the loan

Everything should look like this.

$20,000=\frac{A((1+0.08)^{4}-1) }{0.08(1+0.08)^{4} }$

$20,000=\frac{0.36048896}{0.108839117} A$

$20,000=A(3.31212684)$

$A= 6,038.42$

Now, in order to find the amount paid in interest for the first payment, we just multiply 20,000*0.08= 1,600

And the amount paid to principal is just the payment - interest, that is:

$6,038.42 - $1,600 = $4,438.42

Best of luck.