Question

Youssef just took out a loan from the bank for 78,090 dollars. He plans to repay this loan by making a special payment to the bank of 19,680 dollars in 2 months and by also making equal, regular monthly payments of X. If the interest rate on the loan is 0.63 percent per month, he makes his first regular monthly payment later today, and he makes his last regular monthly payment made in 4 months from today, then what is X, the amount of the regular monthly payment?

Answer 1

Solution :-

Borrowed Amount = $78,090

Present Value of Special Payment = $19,680 / ( 1 + 0.0063 )²

= ( $19,680 * 0.9875 )

= $19,434.36

Now Remaining Balance = $78,090 - $19,434.36 = $58,655.64

Now Regulay monthly payment be X

$58,655.64 = X + [ X / ( 1 + 0.0063 ) ] + [ X / ( 1 + 0.0063 )² ] + [ X / ( 1 + 0.0063 )³ ] + [ X / ( 1 + 0.0063 )⁴ ]  

$58,655.64 = X + ( X * 0.9937 ) + ( X * 0.9875 ) + ( X * 0.981 ) + ( X * 0.975 )

$58,655.64 = X * 4.9378

X = $11,878.94

Therefore the monthly payment = $11,878.94

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