You borrow $1,000 from the bank and agree to repay the loan over the next year in 12 equal monthly payments of $90. However, the bank also charges you a loan initiation fee of $27, which is taken out of the initial proceeds of the loan. What is the effective annual interest rate on the loan, taking account of the impact of the initiation fee? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places. Use a financial calculator or Excel.)

The answer is 1,64%

Explanation:

Since the $27 dollars is taken out of the loan amount the net proceeds we are receiving are $973

We will use the $973 as our Present Value. (PV)

N = 12 which is the number of periods over which repayment takes place. In this case 12 months.

Payments are the monthly replayments of $90 which will be entered in as PMTS.

Thus the following will be entered onto a financial calculator;

N = 12 PMT = -90 PV = 973 FV = 0 COMP I =

Interest = 1,6427 %

rounded we now have an answer of 1,64% using a financial calculator to work out the interest charge

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"we first find value of tax in dollars.

the difference between the two prices   is: 23. 54 - 22 = 1.54

therefore the sales tax in dollars is 1.54

the tax % will be   (amount of tax / original cost price ) × 100

(1.54 / 22) × 100  → (0.07) × 100 =   7

so the tax rate is 7%

we can double check the answer.

7 % of 22   → (7/100) × 22 → 0.07 × 22 = 1.54

22 + 1.54 = 23.54"