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Help Please! I don\'t understand how to get the answer for this one. Thank You f

ID: 1189649 • Letter: H

Question

Help Please! I don't understand how to get the answer for this one. Thank You for the help!

The EZ Credit Company offers to loan a college student $5, 500 for school expenses. Repayment of the loan will be in monthly installments of $229.48 for 30 months. The total repayment of money is $6, 884.40, which includes the original $5, 500, $1, 243.99 in interest charges, and $140.41 for a required life insurance policy covering the amount of the loan. Assume monthly compounding of interest. What nominal interest rate is being charged on this loan? The nominal interest rate that is being charged on this loan is Q% per year. (Round to two decimal places.). The EZ Credit Company offers to loan a college student $5, 500 for school expenses. Repayment of the loan will be in monthly installments of $229.48 for 30 months. The total repayment of money is $6, 884.40, which includes the original $5, 500, $1, 243.99 in interest charges, and $140.41 for a required life insurance policy covering the amount of the loan. Assume monthly compounding of interest. What nominal interest rate is being charged on this loan? The nominal interest rate that is being charged on this loan is Q% per year. (Round to two decimal places.)

Explanation / Answer

Loan payment period (n) = 30 months

Suppose, Monthly interest rate = R

Monthly Loan installment (P) = $229.48

Total loan amount = college loan + insurance payment = $5500 + $140.41 = $5640.41

Thus, as per the formula of present value of annuity,

PV of total loan = PV of all Monthly Loan installment

PV of total loan = P*(1-1/(1+R)^n)/R = 229.48*(1-1/(1+R)^30)/R

At R=1.4%

PV of all Monthly Loan installment = $5590.0756

At R=1.3%

PV of all Monthly Loan installment = $5670.6163

Thus, as per the method of interpolation

R = 1.3% + ((PV of loan at 1.3% - Loan amount)/( PV of loan at 1.3% - PV of loan at 1.4%))*(1.4% - 1.3%)

R = 1.3% + ((5670.6163 - 5640.41)/( 5670.6163 - 5590.0756))*(1.4% - 1.3%)

R = 1.337% approx.

Thus, Annual Nominal interest rate = 12*R = 12*1.337% = 16.044% or 16.04 % approx