Nominal and effective interest rates

[yo091]

e is considering a loan of $35000. His bank has two compound interest rate options:
A: 8.3% per annum, compounding monthly (((ANS: 8.62%)

B: 7.8% per annum, compounding weekly. (ANS: 8.11%)

A. Calculate the effective interest rate for each of the loan options. ANS: 8.62%, ANS: 8.11%
B. Calculate the amount of interest Luke would pay in the first year for each of the loan options.
Which loan should Luke choose and why?
Please help with part B.

[S_R_K]

An effective interest rate of X% p.a. tells you that the interest charged in the first year is X% of the principal.

Assuming Luke wants the cheapest loan (and no other considerations are relevant), he should choose the loan that incurs the least interest.

[NomotivationF]

e is considering a loan of $35000. His bank has two compound interest rate options:
A: 8.3% per annum, compounding monthly (((ANS: 8.62%)

B: 7.8% per annum, compounding weekly. (ANS: 8.11%)

A. Calculate the effective interest rate for each of the loan options. ANS: 8.62%, ANS: 8.11%
B. Calculate the amount of interest Luke would pay in the first year for each of the loan options.
Which loan should Luke choose and why?
Please help with part B.

SRK is correct, i've just added in some working

The effective annual interest rate for loan A is 8.62% and the effective annual interest rate for loan B is 8.11%

For part b, all you have to do is multiply $35000 by the effective interest rate.
For loan A, this would be 35000 x .0862 = $3017
For loan B, this would be 35000 x .0811 = $2838.5

Therefore, Luke should choose loan B, due to the fact that this loan incurs the least interest over the first year.