7. Suppose you are purchasing a vehicle at 5% annual interest. You\'ll make a pa

Question

7. Suppose you are purchasing a vehicle at 5% annual interest. You'll make a payment every month Tor the next 60 months. The vehicle costs $20,000, but you plan to make a $1,000 down payment. a. Using the above information, what would be the monthly payment? Round to 2 decimal places. (2 Points) b. Suppose you want the monthly payment to be $325.00. Using the above information and not changing anything else, what would need to be the annual interest rate? Round to 2 decimal places. (2 Points) c. Suppose you want the monthly payment to be $325.00. Using the above information and not changing anything else, what would need to be the number of monthly payments? Round to 2 decimal places. (2 Points) Co d. Suppose you want the monthly payment to be $325.00. Using the above information and not changing anything else, what would need to be the initial cost of the vehicle? Round to 2 decimal places. (2 Points) e. Suppose you want the monthly payment to be $325.00. Using the above information changing anything else, what would need to be the down payment? Round to 2 decimal places (2 Points)

Explanation / Answer

a) The monthly interest rate will be 5%/12 = 0.41666%

The annuity factor for 0.41666% for 60 months will be 52.99081

Therefore, the mothly payment will be 19000/52.99081 = 358.55 (Since, down payment of 1000 is made, only remaining 19000 should be paid.)

b) Annuity factor should be equal to 19000/325 = 58.46154

Using interpolation, we get 0.0856666 per month. Therefore per annum rate = 0.085666*12 = 1.028%

c) Annuity factor should be equal to 19000/325 = 58.46154

For 5% per annum, how many months annuity will be equal to 58.46154 is the question

For 67 months, it will be 58.3555

For 68 months, it will be 59.1092.

Therefore, it will be between 58 and 59 months. (calculate using interpolation method)

d) Monthly paymnet = 325

Interest = 5% per annum

Therefore, Total payment = 325 * 52.99081 = 17222.01

Therefore, cost = 17222.01 + 1000 = 18222.01

e) Since 18222.01 is less than 19000, there is no need of down payment.

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