Question

A man has borrowed $10,000 which he will repay in 60 equal
monthly installments. After his twenty-fifth payment he desires to
pay the remainder of the loan at the time of the 26th payment in a
single payment. At an interest rate of 2% per month what is the
amount of the payment?

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 | |||||

N= Number of periods | |||||

= [ $10000x0.02 x (1+0.02)^60]/[(1+0.02)^60 -1] | |||||

= [ $200( 1.02 )^60] / [(1.02 )^60 -1 | |||||

=$287.68 | |||||

Step 2 : | Loan due 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 | |||||

n=number of period | |||||

= $287.6796[ 1-(1+0.02)^-35 /0.02] | |||||

= $287.6796[ 1-(1.02)^-35 /0.02] | |||||

= $287.6796[ (0.5) ] /0.02 | |||||

= $7,191.59 | |||||

Step 3 : | Calculation of single payment | ||||

=7191.59*1.02 | |||||

=$7335.42 |

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