Question

3. You are now graduated, got a new well-paid job brand-new car. You stop by at your favorite car car. The sales representative shows you the car and you notice approved for 2.99% APR financing if you pay off your loan approche sales: You storedBota proved for a new well-paid job and have decided to indulge yourself by buying Presentative your favorite vorite car dealership and start negotiating on the terms to buy your % APR fin shows you the car dealership andes you notice that the card price is $35,500. You get of your loan in 5 years and 3.99 if you pay it off in 7 years. a) What is your monthly payment if you pay off your car lo b) What is your monthly payment if you pay off your car loan c) Suppose that you have $35.50 this amount in an ordinary annuity which pas answer. ou pay off your car loan in 5 years? yment if you pay off your car loan in 7 years? you buy your car in cash if you have a chance to invest Mary annuity which pays 7.641.26 for 5 years at the end of each year? Explain your

Answer 1

1. calculation of monthly payment if you payoff your car loan in 5 years:

• APR means Annual percentage rate = 2.99%. That means monthly APR = 2.99/12 = 0.2491%.
• The number of monthly periods in 5 year term is = 5years*12 = 60 months
• Cash outflow today with loan = $35500
• EMI (Equated monthly instalments) = [P*R*(1+R)^{^}N/(1+R)^  N -1]
• EMI = [35500*0.0024916(1+0.0024916)^60/ (1+0.0024916)^59]
• The monthly payment comes to  $637.73 using an EMI calculator.
• Conclusion: - Hence the monthly payment if you payoff your car loan in 5 years = $637.73 per month for 5 years.

2. Calculation of monthly payment if you payoff your car loan in 7 years:

• APR means Annual percentage rate = 3.99%. That means monthly APR = 3.99/12 = 0.3325%.
• The number of monthly periods in 7 year term is = 7years*12 = 84 months
• Cash outflow today with loan = $35500
• EMI (Equated monthly instalments) = [P*R*(1+R)^{^}N/(1+R)^  N -1]
• EMI = [35500*0.003325(1+0.003325)^84/ (1+0.003325)^83]
• The monthly payment comes to  $485 using an EMI calculator.
• Conclusion: - Hence the monthly payment if you payoff your car loan in 7 years = $485 per month for 7 years.

3. Deciding whether to buy car in cash or to invest in 5 year annuity payoff:.

• 5 years APR = 2.99%
• Decision basis: - If the interest received in annuity payoff is more than APR of 2.99%, then it is better of to invest in annuity payoff option.
• using the same EMI calculator and finding for R (interest rate) gives us:
• [P*R*(1+R)^{^}N/(1+R)^  N -1] = 7641.26 (given)
• [35500*R(1+R)^5/ (1+ R)^4 = $7641.26
• R (interest rate) = 2.50%
• Conclusion: Since the interest earned on annuity investment option is less than APR for buying car, it is better to buy car in cash since it will save the APR cost of 2.99% for you and if you invest in annuity option you would have earned only 2.50%.