annie cafe question

Question

annie's café borrows $ 6100 at 6% for 290 day find the total amount must be repaid after 290 days ?

A $ 6129.08

B $ 9007.95

c $ 6466.00

D $ 6394.83

Answer 1

The problem doesn't state the compounding period?

If it is daily compounding, the daily interest rate = .06/365 = .00016438

So, n = 365 and in this case the number of years (t) = 290/365 = .79452

If S = total money to be paid back and S_o = money borrowed, then

S =S_o(1 + I/n)^(nt) = $6100(1.00016438)^(365*.79452) = $6397.81

If the calculation is done on a yearly basis, then S = S_o(1.06)^(.79452) = $6389.04 I'd choose D !