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?

Homework Answers

Answer #1
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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