1. You take out a 2-year, $3,750 loan at 10% simple annual interest. The lender
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Question
1. You take out a 2-year, $3,750 loan at 10% simple annual interest. The lender charges you a $150 fee. Thinking of the fee as additional interest, what is the actual annual interest rate r you will pay?
2.You are expecting a tax refund of $4,000 in 10 weeks. A tax preparer offers you an "interest-free" loan of $4,000 for a fee of $50 to be repaid by your refund check when it arrives in 10 weeks. Thinking of the fee as interest, what simple interest rate would you be paying on this loan? HINT [See Example 6.] (Round your answer to three decimal places.)
3.At auction, 3-month T-bills were sold at a discount of 3.530%. What was the simple annual yield r? HINT [See Example 5.] (Round your answer to three decimal places.)
Explanation / Answer
1) Interest amount= P*t* r = 3750 * 2* 0.1 =750
Amount = P+I =3750+750 =4500
Amount with charges= 4500+150 =4650
To calculate rate of interest:
I= P*r *t and A= P + I
then, A = P + P*r*t
A- P = P*r*t => r = (A-P) / P*t => r = (4650-3750) / (3750*2)
r = 0.12
r=12%
2) Rate of interest= (100*Interest) /(Principal* Time)
Interest= 50
principal= 4000
Time =10 /52 per year
Rate of interest= (100*50) / (4000*(10/52))
Rate of interest= 5000/769.2308= 6.5
Rate of interest= 6.5%
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