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A radio commercial for a loan company states: “You only pay $0.29 a day for

each $500 borrowed.” If you borrow $1,500 for 120 days, what amount will you

repay, and what annual interest rate is the company actually charging?

Verified Answer :

nobillionaireNobley

A loan of $1500 attracts a daily interest of 3(0.29) = $0.87
For 120 days you pay $0.87 x 120 = $104.40 interest.

I = PrT; where P is the principal, r is the annual interest rate and T is the time.
500 x r x 1/365 = 0.29
r = 0.29 x 365 / 500 = 105.85/500 = 0.2117

Therefore,, Annual interest rate = 21.17%

the amount that they charge for $ 1500 would be :

$0.29 x 3 = $ 0.87

Total charge for 120 days would be : 
$0.87 x $ 120 = $ 104.4

The amount that should be repaid : 1500 + 104.4   = 1604.4

Interest rate = 
a = p(1+rt)
1604.4 = 1500 ( 1 +  r*120/365)

r = 21.17 %

Hope this helps


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