Question

1 Lupe made a down payment of $5000 toward the purchase of a new car. To pay the balance of the purchase price, she has secured a loan from her bank at the rate of 6%/year compounded monthly. Under the terms of her finance agreement she is required to make payments of $440/month for 36 mo. What is the cash price of the car?

2. Find the amount (future value) of the ordinary annuity. (Round your answer to the nearest cent.) $850/month for 18 years at 6%/year compounded monthly

3 Lupe made a down payment of $5000 toward the purchase of a new car. To pay the balance of the purchase price, she has secured a loan from her bank at the rate of 8%/year compounded monthly. Under the terms of her finance agreement she is required to make payments of $440/month for 36 mo. What is the cash price of the car?

(only answered needed)

Answer 1

Question 1:

Down payment = $5,000

P = monthly loan payment = $440

r = monthly interest rate = 6%/12 = 0.5%

n = 36 months

Loan Amount = P * [1 - (1+r)^-n] / r

= $440 * [1 - (1+0.5%)^-36] / 0.5%

= $440 * 0.16435508119 / 0.005

= $14,463.2471453

Price of car = Down payment + loan amount = $5,000 + $14,463.25 = $19,463.25

Question 2:

P = Monthly amount = $850

r = monthly interest rate = 6%/12 = 0.5%

n = 18*12 = 216 months

Future Value of ordinary annuity = P * [(1+r)^n - 1] / r

= $850 * [(1+0.5%)^216 - 1] / 0.5%

= $850 * 1.93676597204 / 0.005

= $329,250.215246

Therefore, future value of ordinary annuity is $329,250.22

Question 3:

Down payment = $5,000

P = monthly loan payment = $440

r = monthly interest rate = 8%/12 = 0.66666667%

n = 36 months

Loan Amount = P * [1 - (1+r)^-n] / r

= $440 * [1 - (1+0.66666667%)^-36] / 0.66666667%

= $440 * 0.21274537006 / 0.0066666667

= $14,041.1944174

Price of car = Down payment + loan amount = $5,000 + $14,041.19 = $19,041.19