Question

When Cecilia's car needs a new transmission, she's stuck with a bill for $1840. The dealership offers her an 18-month loan at 14.5% interest to be repaid in 18equal installments. Find the monthly payment. Round your intermediate steps to the nearest cent.The monthly payment is?

Answer 1

Cecilia's monthly payment for the loan with an 18-month term and a 14.5% annual interest rate will be approximately $103.87.

Step-by-step explanation:

When Cecilia gets a loan for a new transmission, she's presented with a repayment plan that involves an 18-month loan at 14.5% interest with 18 equal payments. To calculate the monthly payment, we use the formula for an amortizing loan which is:

P = (Pr * r) / (1 - (1 + r)^(-n))

Where:

• P is the monthly payment
• Pr is the principal amount ($1840)
• r is the monthly interest rate (14.5% annual rate divided by 12 months)
• n is the total number of payments (18)

Calculating the monthly interest rate: r = 14.5% / 12 = 1.2083% or 0.012083 (in decimal form)

Plugging in the values into the formula:

P = (1840 * 0.012083) / (1 - (1 + 0.012083)^(-18))

Carrying out the calculation:

P = ($22.23) / (1 - (1.012083)^(-18))

Calculating the denominator (rounded to two decimal places for each step as required):

P = $22.23 / (1 - 0.78599)

P = $22.23 / 0.21401

P = $103.87

Therefore, Cecilia's monthly payment will be approximately $103.87.

Answer 2

Explanation

The data given are:

The present value, Pv = $1840

Rate, r = 14.5% = 14.5/100 = 0.145

The time is 18 months, and in years, t = 18/12 = 1.5 years

Since the Present value is known, then the future value can be calculated by the formula:

`\begin{gathered} Fv=Pv(1+r)^n \\ Fv=1840(1+0.145)^(1.5) \\ Fv=1840*1.225 \\ Fv=2254 \end{gathered}`

So to know the monthly installment payment, we divide Future value by 18, that is,

`(2254)/(18)=125.22`

Therefore the monthly payment is $125.22