A 50000 loan made on january 1 ,2010 is to br repaid over 25 years with payments

Question

A 50000 loan made on january 1 ,2010 is to br repaid over 25 years with payments on the last day of each month,beginig january 31, 2010

a)if i2=10%, find the amount of monthly payment X

b) starting with first payment, the borrower decided to pay an additiona; 100 per month, on top of the regular payment of X,until the loan is repaid.An additional fractional payment might be necessary one month after the last reqular payment of X+100.On what date will the final payment of X+100 be made, and what will be the amount of the additional fractional payment?

Explanation / Answer

Answer :

(a) monthly rate j=(1+i)1/12 - 1 where i is annual rate and now

1+ i = [1 + i(2) /2 ]2 , then j = (1+0.1/2)1/6 - 1

since X is monthly payment,

Xa300 | j = 50,000

X = 447.24

(b) if (X+100)an | j = 50,000, then n=168.5

168th payment occurs on Dec 31, 2023 by X + 100 = 547.24

The fractional part 50,000 - 547.240a168 | j = Yv j 169 then Y=290.30.

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