Question

Question 4 25 pts A student borrowed $9000 from the bank. She must pay $300 at the end of every month for 5 years. What is the effective annual interest rate on the loan? Margin of error: +/-0.01 NOTE: submit answer in decimal form, not as a percentage. Example: if answer is 4% submit 0.04

Answer 1

Answer:

Explanation: To find the rate of Interest we use following formula PV =42-6) TP) where. PV = Initial Amount OR Initial Deposit OR Initial Investment OR Amount at time zero A = Regular Withdrawal Amount OR Regular interest OR Regular Dividend OR Installment Amount n = Number of Years/Period r = Compound Interest Rate IP-Annual Nominal Rate of Interest Given: Number of Periods/Years (n) = 5 Initial Investement (PV) = $9000 Regular Withdrawal (A) = $3600 Benefit paid annually A = 300 * 12 = 3600 After substituting the values into the formula we have PV = 44 ", 9000 = 3600 • 1-477) POP)

1-G (P) ) 9000 3600 Discount Factor 1-6)* _9000 - 2.5 (P) 3600

We can find the interest rate by linear interpolation using the guessed interest rates of 36.1 % and 37.1 % using the formula T=rı + (12-1)(DF - DP) DF - DF Where. r = Interest Rate (value to be found) r = First guess of interest rate = 36.1% = 0.361 r2 = Second guess of Interest rate = 37.1% = 0.371 DF = Discount factor (Calculated from present value and periodical payments) = 2.5 DF, = Discount factor (Calculated from first guess of interest rate) DF, Discount factor (Calculated from second guess of interest rate) .)" - G DE: DF = ? per 1- 0.361 -251865 12+((1+0.361)1/12 1) DF, -- )" 1-Gast) 12+((1+0.371)1/12 - 1) 2.48353

Subtituting the values in given formula for r. T="i+ (ra-1)(DF-DF) DF - DF (0.371 0.361)(2.5 2.51865) 2.48353-2.51865 = 0.36586 = 36.58604% The rate of interest is 36.58604%