The new car costs $19,999. Two options; 1) down payment of 20% and finance the b

Question

The new car costs $19,999. Two options; 1) down payment of 20% and finance the balance with no interest and payments for the first few months, 2) or get a rebate of $1,000 if pays cash. The financing alternative would require to pay $460 a month for two years starting at the beginning of the 12th month. My savings account, which pays 4.5% interest per annum compounded monthly, shows a balance large enough to pay cash for the car. a) What is the opportunity cost of the cash option over the first year? b) What is the cost of the financing alternative? c) What is the cost of the cash option?

Explanation / Answer

A) Opportunity cost of cash option is the interest forgone @ 4.5 %

interest forgone =

The formula for annual compound interest is A = P (1 + r/n) ^ nt:

Where:

A = the future value of the investment/loan, including interest
P = the principal investment amount (the initial deposit or loan amount)
r = the annual interest rate (decimal)
n = the number of times that interest is compounded per year
t = the number of years the money is invested or borrowed for

            = 18999 ( 1+0.045/12)12

              = 19872

opportunity cost = 19872-18999

                         = $ 873

b)Cost of financing alternative

cost                 = 19999

down payment @ 20%             = 4000

installment 460*24months         =11040

total cost under financing =                               $15040

c) cost of the cash option = cost - rebate

                                      = 19999-1000

                                      = $ 18999

=

note : as the installment payments = 460 * 24 months = $11040,

i beleave that the installment amount must be mor that 460

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