Question

juan borrowed money from an online lending company to invest in rare coins. he took out a personal, amortized loan for $20,000, at an interest rate of 7.15%, with monthly payments for a term of 2 years. for each part, do not round any intermediate computations and round your final answers to the nearest cent. if necessary, refer to the list of financial formulas. (a) find juans monthly payment. $ (b) if juan pays the monthly payment each month for the full term, find his total amount to repay the loan. $ (c) if juan pays the monthly payment each month for the full term, find the total amount of interest he will pay. $

Explanation:

Step1: Identify loan - related values

$P = 20000$ (loan principal), $r=0.0715$ (annual interest rate), $n = 12$ (number of payments per year), $t = 2$ (number of years)

Step2: Calculate the monthly interest rate

$i=\frac{r}{n}=\frac{0.0715}{12}$

Step3: Calculate the number of payments

$m=n\times t=12\times2 = 24$

Step4: Use the amortized - loan payment formula

The formula for the monthly payment $M$ of an amortized loan is $M=\frac{P\times i\times(1 + i)^m}{(1 + i)^m-1}$
Substitute the values:
$M=\frac{20000\times\frac{0.0715}{12}\times(1+\frac{0.0715}{12})^{24}}{(1+\frac{0.0715}{12})^{24}-1}$
$M\approx897.94$

Step5: Calculate the total amount to repay

The total amount to repay $A = M\times m$
$A=897.94\times24 = 21550.56$

Step6: Calculate the total interest paid

The total interest $I=A - P$
$I=21550.56-20000=1550.56$

Answer:

(a) $\$897.94$
(b) $\$21550.56$
(c) $\$1550.56$