using technology, determine the monthly payment on a 35 month loan of $28,000 at 8.1% compounded monthly…

Explanation:

Step1: Identify the loan - payment formula

The formula for the monthly payment of a loan is $M = P\frac{r(1 + r)^n}{(1 + r)^n-1}$, where $M$ is the monthly payment, $P$ is the principal amount of the loan, $r$ is the monthly interest rate, and $n$ is the total number of payments. First, convert the annual interest rate to a monthly interest rate. The annual interest rate $i = 8.1%=0.081$, so the monthly interest rate $r=\frac{0.081}{12}=0.00675$. The principal amount $P = 28000$, and the number of payments $n = 35$.

Step2: Substitute values into the formula

Substitute $P = 28000$, $r=0.00675$, and $n = 35$ into the formula: [ \begin{align*} M&=28000\times\frac{0.00675(1 + 0.00675)^{35}}{(1 + 0.00675)^{35}-1}\ \end{align*} ] First, calculate $(1 + 0.00675)^{35}$. Using the formula $a^b$, where $a = 1.00675$ and $b = 35$, we get $(1 + 0.00675)^{35}\approx1.26097$. Then, $0.00675\times(1 + 0.00675)^{35}=0.00675\times1.26097\approx0.00851265$. $(1 + 0.00675)^{35}-1\approx1.26097 - 1=0.26097$. $\frac{0.00675(1 + 0.00675)^{35}}{(1 + 0.00675)^{35}-1}=\frac{0.00851265}{0.26097}\approx0.032617$. $M = 28000\times0.032617\approx913.28$.

However, if we use a financial - calculator or an online loan - payment calculator:

• $N = 35$ (number of periods)
• $I/Y=8.1$ (annual interest rate)
• $PV=- 28000$ (present value, negative because it's the amount received)
• $FV = 0$ (future value of the loan is 0 after all payments are made)
• $P/Y = 12$ (payments per year)
• $C/Y = 12$ (compounding periods per year)

The calculated monthly payment $M\approx900.90$.

Answer:

$900.90$