Question

As in Problem 1, once again, you are borrowing $6500 to purchase a car. However, now the first payment is due immediately. There will be a total of 36 monthly payments (The first payment occurs immediately. The remaining 35 occur at the end of each of the following months). The advertised interest rate is 9% APR (therefore use a monthly discount rate of r-0.75% in your computations). The payments will all be equal in size HINT: This is an annuity due problem. Make sure you understand the discussion in the book, especially Example 5B - paying attention to Footnote 3 (which applies to Parts B, C, and D). Also work the Annuity Due problems at the end of the chapter before you work this problem Part A) What is the size of the first payment? (which vou pay immediately) Part B)Now assume that the size of the car payments increases by 2% every month. size of the first payment? What is the Part C) Now assume that the size of the car payments decreases by 2% every month. What is the size of the 4th (fourth) payment? Hint: The answer is NOT $259.45 Part D) Now assume that the size of the car payments decrease by 0.75% every month. What is the size of the payment that occurs 15 months from today? Part E) Now assume that the size of the car payments increases by 0.75% every month. What is the size of the payment that occurs 15 months from today?
help!! I know this is technically two problems but I ran out of question so please help if you can. I don't have anymore questions left!

also posting problem 1 as an reference but just help to the top 2

Answer 1

(a) Amount Borrowed = $ 6500, Borrowing Tenure = 36 months, APR = 9 % or 0.75 % per month

Let the equal monthly installments be $ K

Therefore, 6500 = K x (1/0.0075) x [1-{1/(1.0075)^(36)}] x (1.0075)

K = $ 205.16

(b) If the monthly payments increase by 2 %, it is a case of growing annuity due. The same can be solved as shown below:

Let the first payment be $ M

Therefore, 6500 = [M / (Discount Rate - Growth Rate)] x [1 - {(1+growth rate) / (1+Discount rate)}^(n)] where n is the tenure, discount rate is the interest rate per period and growth rate is the rate at which the periodic payments grow

6500 = [M / (0.0075 - 0.02)] x [1-{(1.02) / (1.0075)}^(36)] x (1.0075)

M = $ 144.32

(c) If the monthly payments decrease by 2 % the calculations remain the same with only the growth rate being - 2 %.

Let the first payment be $ N

Therefore, 6500 = [N / (0.0075 - (-0.02))] x [1-{(0.98) / (1.0075)}^(36)] x (1.0075)

N = $ 281.28

Fourth Payment = 281.28 x (1-0.02)^(3) = $ 264.74 (the power of the multiplicative factor is 3 and not 4, because all payments are received at the beginning of the period, Hence, the fourth payment comes in at the end of month 3 and not month 4)

(d) The calculations for this part will be similar to the previous part's, with the growth rate being -0.75 %

Let the first payment be $ L

Therefore, 6500 = [L / (0.0075 - (-0.0075))] x [1-{(0.9925) / (1.0075)}^(36)] x (1.0075)

L = $ 231.93

Payment Size 15 months from now (size of the 16th payment as it is an annuity due) = 231.93 x (1-0.0075)^(15) = $ 207.16

NOTE: Please raise separate queries for solutions to the other questions and sub-parts as one query is restricted to the solution of only one question upto a maximum of four sub-parts.