Question

# A bank recently loaned you \$14,015.00 to buy a car. The loan is for 4 years...

A bank recently loaned you \$14,015.00 to buy a car. The loan is for 4 years in is fully amortized. The nominal rate on the loan is 11%, and payments are made at the end of each month. What will be the remaining balance on the loan after you make payment number 25?

 Step 1 : EMI = [P x R x (1+R)^N]/[(1+R)^N-1] Where, EMI= Equal Monthly Payment P= Loan Amount R= Interest rate per period =11%/12 =0.9166667% N= Number of periods =12*4 =48 = [ \$14015x0.0091666667 x (1+0.0091666667)^48]/[(1+0.0091666667)^48 -1] = [ \$128.4708338005( 1.0091666667 )^48] / [(1.0091666667 )^48 -1 =\$362.2249 Step 2 : Calcualtion of loan amount after 25th payment Present Value Of An Annuity = C*[1-(1+i)^-n]/i] Where, C= Cash Flow per period i = interest rate per period =11% /12 =0.916667% n=number of period =48-25 =23 = \$362.2249[ 1-(1+0.009166667)^-23 /0.009166667] = \$362.2249[ 1-(1.009166667)^-23 /0.009166667] = \$362.2249[ (0.1893) ] /0.009166667 = \$7,480.78

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