To Solve the given question you just need to apply the formula for effective annual interest rate i.e. (EAR)

Which is;

EAR (effective annual rate) | = | (1 + (nominal interest rate / number of compounding periods)) ^ (number of compounding periods) – 1 |

Check the below mentioned data for detailed solution.

Thanks

1. (a) Calculation of effective annual interest rate for each 48-month option :- EAR (effective annual rate) (1 + (nominal interest rate / number of compounding periods)) ^ (number of compounding periods) - 1 Car dealer (48 month) 8.50% Nominal interest rate Number of compunding periods 12 EAR (1 + (0.085 / 12)) ^ (12) - 1 EAR 8.84% Credit union (48 month) 9.30% Nominal interest rate Number of compunding periods 4 EAR (1 + (0.093/4))^(4) - 1 EAR 9.63% Bank (48 month) 9.10% Nominal interest rate Number of compunding periods 2 EAR (1 + (0.091 / 2)) ^ (2) - 1 EAR 9.31%

(b) Calculation of savings made by choosing best option over the worst option :- Since the EAR of car dealer is least it is the best option for 48 month period & similarly Credit union has highest EAR it is worst Loan amount = Cost of car-Deposit account-borrowing from parents 27650-7500-5000 15140 =(loan amount)* (EAR)*(years) Total interest to be paid under credit union option for 48 month financing (A) =(15140)*(0.0963)*(4) 5835.78 =(loan amount)* (EAR)*(years) Total interest to be paid under car dealer option for 48 month financing (B) =(15140)*(0.0884)*(4) 5357.04 Saving from choosing best option over worst (A-B) 478.74

2.

(a) Calculation of effective annual interest rate for each 36-month option :- EAR (effective annual rate) (1 + (nominal interest rate / number of compounding periods)) ^ (number of compounding periods) - 1 Credit union (36 month) 9.00% Nominal interest rate Number of compunding periods 4 EAR (1 + (0.090 / 4))^(4) - 1 EAR 9.31% Bank (48 month) 8.80% Nominal interest rate Number of compunding periods 2 EAR (1 + (0.091 / 2)) ^ (2) - 1 EAR 8.99%

(b) Calculation of savings made by choosing better option :- Since the EAR of Credit union is less than the Bank hence, Credit union is better option for 36 month period Loan amount = Cost of car-Deposit account-borrowing from parents 27650-7500-5000 15140 I =(loan amount)*(EAR)*(years) Total interest to be paid under Credit union option for 36 month financing (C) =(15140)*(0.0931)*(3) II 4231.4 = =(loan amount)*(EAR)*(years) Total interest to be paid under Bank option for 48 month financing (D) 11 =(15140)*(0.0899)*(3) = 4085.96 Saving from choosing better option (C-D) II 145.44

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