Question

A salesperson gives you the following payment plans, "Buy this new car for $30,000 cash OR, with an appropriate down payment, pay $800 per month for 36 months at 5% interest.". If these two offers are financially equivalent at the stated interest rate, calculate the "appropriate" down payment. (Remember, when interest rates are quoted as they are in this question, they are APRs. Also, Financially equivalent means that the two streams of cashflows have the same PV)

Answer 1

Appropriate down payment is $ 3307 Explanation: We have to apply sandbly equal monthly Installment EMI) formula to Gledate down payment: tet t' be the down payment amount of Total Amo unt to be pald $ 30000 EA Principal amount borrowed = p = Amount paid - Down Payment . P= $(30000 - 2) Monthly Installment = 5 EMI = $ 800 per month. peu . cost Annualised interest rate = 5.1. Monthly interest rates with -X 1100 on 0.0041667 * =r Tenure or number of period -- 36 months EMI = P xgx (4+ ogni (178)n-1

800 - $ 800 = $( 30 000 ->) * 0.00111667 x 11+0.0041667)36 (1 to 0041 667)36 1 (30,000-x) *00041667 X (14004166736 (1.0041667)36 (30000 -> ) x 0:0041667 x 1.161473619 1.1614736 19-1 800 1.1614 73619 800 - 130000 - X X 0.0041667 X 0.161423019 800 - (30000 - 31 X0.0041667 x 7.192.962 800 = 130.000-) x 0.02997 (30.000-X) 800 0.02997 (30.000-x) = 26693 2: $30000 - $26693 . $ 3307 The Appropriate down payment is $3307.

P= Principal Amount borrowed $ 26693 $ 3307 X= Down Payment made EMI = Equal monthly Install ment = $800 A = Total Amount bald $ 30 000 rate of interest per month & SXL = 0.0041687 n= Number of Payment Period / Tenure of Payment Period = 36 12 too